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New existence results for conjoined bases of singular linear Hamiltonian systems with given Sturmian properties
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2024
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Peter Šepitka
Roman Šimon Hilscher
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+
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Contributions to Generalized Oscillation Theory of Linear Hamiltonian Systems
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2024
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Peter Šepitka
Roman Šimon Hilscher
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+
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Note on singular Sturm comparison theorem and strict majorant condition
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2024
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Peter Šepitka
Roman Šimon Hilscher
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+
PDF
Chat
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Generalized focal points and local Sturmian theory for linear Hamiltonian systems
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2023
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Peter Šepitka
Roman Šimon Hilscher
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+
PDF
Chat
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Comparative index and Hörmander index in finite dimension and their connections
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2023
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Julia Elyseeva
Peter Šepitka
Roman Šimon Hilscher
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+
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Solutions with prescribed numbers of focal points of nonoscillatory linear Hamiltonian systems
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2022
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Peter Šepitka
Roman Šimon Hilscher
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+
PDF
Chat
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Oscillation Numbers for Continuous Lagrangian Paths and Maslov Index
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2022
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Julia Elyseeva
Peter Šepitka
Roman Šimon Hilscher
|
+
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Weak disconjugacy, weak controllability, and genera of conjoined bases for linear Hamiltonian systems
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2022
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Peter Šepitka
Roman Šimon Hilscher
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+
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Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval
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2021
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Peter Šepitka
Roman Šimon Hilscher
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+
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Comparative index and Lidskii angles for symplectic matrices
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2021
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Peter Šepitka
Roman Šimon Hilscher
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+
PDF
Chat
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Transformation preserving controllability for nonlinear optimal control problems with joint boundary conditions
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2021
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Roman Šimon Hilscher
Vera Zeidan
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+
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Oscillation numbers for continuous Lagrangian paths and Maslov index
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2021
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Julia Elyseeva
Peter Šepitka
Roman Šimon Hilscher
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+
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Distribution and number of focal points for linear Hamiltonian systems
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2020
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Peter Šepitka
Roman Šimon Hilscher
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+
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Sturmian comparison theorems for completely controllable linear Hamiltonian systems in singular case
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2020
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Peter Šepitka
Roman Šimon Hilscher
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+
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Singular Sturmian comparison theorems for linear Hamiltonian systems
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2020
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Peter Šepitka
Roman Šimon Hilscher
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+
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Antiprincipal solutions at infinity for symplectic systems on time scales
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2020
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Iva Dřímalová
Roman Šimon Hilscher
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+
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Difference Equations and Discrete Dynamical Systems with Applications
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2020
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Martin Böhner
Stefan Siegmund
Roman Šimon Hilscher
Petr Stehlík
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+
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Miscellaneous Topics on Symplectic Systems
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2019
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Ondřej Došlý
Julia Elyseeva
Roman Šimon Hilscher
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+
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Symplectic Difference Systems: Oscillation and Spectral Theory
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2019
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Ondřej Došlý
Julia Elyseeva
Roman Šimon Hilscher
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+
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Basic Theory of Symplectic Systems
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2019
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Ondřej Došlý
Julia Elyseeva
Roman Šimon Hilscher
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+
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Oscillation Theory of Symplectic Systems
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2019
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Ondřej Došlý
Julia Elyseeva
Roman Šimon Hilscher
|
+
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Comparative Index Theory
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2019
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Ondřej Došlý
Julia Elyseeva
Roman Šimon Hilscher
|
+
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Motivation and Preliminaries
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2019
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Ondřej Došlý
Julia Elyseeva
Roman Šimon Hilscher
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+
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Discrete Symplectic Eigenvalue Problems
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2019
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Ondřej Došlý
Julia Elyseeva
Roman Šimon Hilscher
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+
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Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems
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2018
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Peter Šepitka
Roman Šimon Hilscher
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+
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Singular Sturmian separation theorems for nonoscillatory symplectic difference systems
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2018
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Peter Šepitka
Roman Šimon Hilscher
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+
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Discrete oscillation theorems for symplectic eigenvalue problems with general boundary conditions depending nonlinearly on spectral parameter
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2018
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Julia Elyseeva
Roman Šimon Hilscher
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+
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Focal points and principal solutions of linear Hamiltonian systems revisited
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2018
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Peter Šepitka
Roman Šimon Hilscher
|
+
PDF
Chat
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Sufficiency and sensitivity for nonlinear optimal control problems on time scales via coercivity
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2017
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Roman Šimon Hilscher
Vera Zeidan
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+
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On square integrable solutions and principal and antiprincipal solutions for linear Hamiltonian systems
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2017
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Roman Šimon Hilscher
Petr Zemánek
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+
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Dominant and recessive solutions at infinity and genera of conjoined bases for discrete symplectic systems
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2017
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Peter Šepitka
Roman Šimon Hilscher
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+
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Comparative index and Sturmian theory for linear Hamiltonian systems
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2016
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Peter Šepitka
Roman Šimon Hilscher
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+
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Sturm–Liouville matrix differential systems with singular leading coefficient
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2016
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Iva Dřímalová
Werner Kratz
Roman Šimon Hilscher
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+
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Principal solutions at infinity for time scale symplectic systems without controllability condition
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2016
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Peter Šepitka
Roman Šimon Hilscher
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+
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Genera of conjoined bases of linear Hamiltonian systems and limit characterization of principal solutions at infinity
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2016
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Peter Šepitka
Roman Šimon Hilscher
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+
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Reid’s Construction of Minimal Principal Solution at Infinity for Linear Hamiltonian Systems
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2016
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Peter Šepitka
Roman Šimon Hilscher
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+
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Principal and antiprincipal solutions at infinity of linear Hamiltonian systems
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2015
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Peter Šepitka
Roman Šimon Hilscher
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+
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Time scale symplectic systems with analytic dependence on spectral parameter
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2015
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Roman Šimon Hilscher
Petr Zemánek
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+
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Eigenvalue Comparison for Discrete Symplectic Systems
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2015
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Roman Šimon Hilscher
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+
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Asymptotic properties of solutions of Riccati matrix equations and inequalities for discrete symplectic systems
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2015
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Roman Šimon Hilscher
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+
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Recessive solutions for nonoscillatory discrete symplectic systems
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2014
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Peter Šepitka
Roman Šimon Hilscher
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+
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Limit circle invariance for two differential systems on time scales
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2014
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Roman Šimon Hilscher
Petr Zemánek
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+
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Principal Solutions at Infinity of Given Ranks for Nonoscillatory Linear Hamiltonian Systems
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2014
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Peter Šepitka
Roman Šimon Hilscher
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+
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Limit point and limit circle classification for symplectic systems on time scales
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2014
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Roman Šimon Hilscher
Petr Zemánek
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+
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Minimal Principal Solution at Infinity for Nonoscillatory Linear Hamiltonian Systems
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2014
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Peter Šepitka
Roman Šimon Hilscher
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+
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Generalized Lagrange Identity for Discrete Symplectic Systems and Applications in Weyl–Titchmarsh Theory
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2014
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Roman Šimon Hilscher
Petr Zemánek
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PDF
Chat
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Weyl disks and square summable solutions for discrete symplectic systems with jointly varying endpoints
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2013
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Roman Šimon Hilscher
Petr Zemánek
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+
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Weyl–Titchmarsh theory for discrete symplectic systems with general linear dependence on spectral parameter
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2013
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Roman Šimon Hilscher
Petr Zemánek
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+
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Comparison theorems for self-adjoint linear Hamiltonian eigenvalue problems
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2013
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Roman Šimon Hilscher
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A Generalized Index Theorem for Monotone Matrix-Valued Functions with Applications to Discrete Oscillation Theory
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2013
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W. Kratz
Roman Šimon Hilscher
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+
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Oscillation and spectral theory of Sturm-Liouville differential equations with nonlinear dependence in spectral parameter
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2013
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Roman Šimon Hilscher
Román
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+
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Eigenvalue theory for time scale symplectic systems depending nonlinearly on spectral parameter
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2012
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Roman Šimon Hilscher
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Oscillation theorems for discrete symplectic systems with nonlinear dependence in spectral parameter
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2012
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Roman Šimon Hilscher
|
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PDF
Chat
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Spectral and oscillation theory for general second order Sturm-Liouville difference equations
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2012
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Roman Šimon Hilscher
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Oscillation criterion for half-linear differential equations with periodic coefficients
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2012
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Ondřej Došlý
Abdullah Özbekler
Roman Šimon Hilscher
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+
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Oscillation and spectral theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter
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2012
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Martin Böhner
Werner Kratz
Roman Šimon Hilscher
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+
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Oscillation theorems and Rayleigh principle for linear Hamiltonian and symplectic systems with general boundary conditions
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2012
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Roman Šimon Hilscher
Vera Zeidan
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+
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New results for time reversed symplectic dynamic systems and quadratic functionals
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2012
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Roman Šimon Hilscher
Petr Zemánek
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+
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First order conditions for generalized variational problems over time scales
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2011
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Roman Šimon Hilscher
Vera Zeidan
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PDF
Chat
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Rayleigh principle for linear Hamiltonian systems without controllability
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2011
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Werner Kratz
Roman Šimon Hilscher
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+
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Sturmian theory for linear Hamiltonian systems without controllability
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2011
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Roman Šimon Hilscher
|
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PDF
Chat
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Weyl-Titchmarsh Theory for Time Scale Symplectic Systems on Half Line
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2011
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Roman Šimon Hilscher
Petr Zemánek
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+
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Overview of Weyl-Titchmarsh Theory for Second Order Sturm-Liouville Equations on Time Scales
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2011
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Roman Šimon Hilscher
Petr Zemánek
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+
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Eigenvalue and oscillation theorems for time scale symplectic systems
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2011
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Werner Kratz
Roman Šimon Hilscher
Vera Zeidan
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+
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Rayleigh principle for time scale symplectic systems and applications
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2011
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Roman Šimon Hilscher
Vera Zeidan
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+
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On general Sturmian theory for abnormal linear Hamiltonian systems
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2011
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Roman Šimon Hilscher
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Eigenvalue and oscillation theorems for time scale symplecticsystems
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2011
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Werner Kratz
Roman Šimon Hilscher
Vera Zeidan
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+
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Reid Roundabout Theorems for Time Scale Symplectic Systems
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2010
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Roman Šimon Hilscher
Vera Zeidan
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+
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Nabla time scale symplectic systems and related quadratic functionals
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2010
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Roman Šimon Hilscher
Vera Zeidan
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PDF
Chat
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Symmetric Three-Term Recurrence Equations and Their Symplectic Structure
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2010
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Roman Šimon Hilscher
Vera Zeidan
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+
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Symplectic Structure of Jacobi Systems on Time Scales
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2010
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Roman Šimon Hilscher
Vera Zeidan
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+
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Abstract Book of CDEIT 2010
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2010
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Zuzana Došlá
Robert Mařı́k
Roman Šimon Hilscher
Jiří Šremr
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+
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Colloquium on Differential Equations and Integration Theory
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2010
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Zuzana Došlá
Robert Mařı́k
Roman Šimon Hilscher
Jiří Šremr
Simona Fišnarová
Milan Tvrdý
Karel Lepka
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PDF
Chat
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Friedrichs extension of operators defined by linear Hamiltonian systems on unbounded interval
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2010
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Roman Šimon Hilscher
Petr Zemánek
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+
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Picone type identities and definiteness of quadratic functionals on time scales
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2009
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Roman Šimon Hilscher
Vera Zeidan
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+
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Multiplicities of focal points for discrete symplectic systems: revisited
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2009
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Roman Šimon Hilscher
Vera Zeidan
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+
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International Conference on Differential Equations and Their Applications (Equadiff 12)
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2009
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Roman Šimon Hilscher
Ondřej Došlý
Jan Čermák
Josef Diblı́k
Zuzana Došlá
Robert Hakl
Karel Lepka
Alexander Lomtatidze
P. Řehák
Zdeněk Šmarda
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Definiteness of quadratic functionals for Hamiltonian and symplectic systems: A survey
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2009
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Roman Šimon Hilscher
Petr Zemánek
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+
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Differentiation of solutions of dynamic equations on time scales with respect to parameters
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2009
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Roman Šimon Hilscher
Werner Kratz
Vera Zeidan
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+
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Eigenvalue, oscillation, and variational results for time scale symplectic systems
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2009
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Roman Šimon Hilscher
Román
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+
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Oscillation results for time scale symplectic systems
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2009
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Roman Šimon Hilscher
Vera Zeidan
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+
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Trigonometric and hyperbolic systems on time scales
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2009
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Roman Šimon Hilscher
Petr Zemánek
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+
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Terminal value problems for first and second order nonlinear equations on time scales
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2008
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Roman Šimon Hilscher
Christopher C. Tisdell
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+
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Weak maximum principle and accessory problem for control problems on time scales
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2008
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Roman Šimon Hilscher
Vera Zeidan
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PDF
Chat
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Time scale embedding theorem and coercivity of quadratic functionals
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2008
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Roman Šimon Hilscher
Vera Zeidan
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+
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Riccati equations for abnormal time scale quadratic functionals
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2007
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Roman Šimon Hilscher
Vera Zeidan
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LEGENDRE, JACOBI, AND RICCATI TYPE CONDITIONS FOR TIME SCALE VARIATIONAL PROBLEM WITH APPLICATION
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2007
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Roman Šimon Hilscher
Vera Zeidan
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Applications of time scale symplectic systems without normality
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2007
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Roman Šimon Hilscher
Vera Zeidan
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+
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PERTURBATION OF NONNEGATIVE TIME SCALE QUADRATIC FUNCTIONALS
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2007
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Roman Šimon Hilscher
Viera Štoudková Růžičková
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Perturbation of time scale quadratic functionals with variableendpoints
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2007
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Roman Šimon Hilscher
Viera Štoudková Růžičková
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Extension of Discrete LQR-Problem to Symplectic Systems ∗
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2007
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Roman Šimon Hilscher
Vera Zeidan
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+
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Coupled intervals for discrete symplectic systems
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2006
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Roman Šimon Hilscher
Vera Zeidan
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+
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Time scale symplectic systems without normality
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2006
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Roman Šimon Hilscher
Vera Zeidan
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+
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Implicit Riccati equations and quadratic functionals for discrete symplectic systems
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2006
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Roman Šimon Hilscher
Viera Štoudková Růžičková
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Colloquium on Differential and Difference Equations
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2006
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Ondřej Došlý
Zuzana Došlá
P. Řehák
Roman Šimon Hilscher
Miroslav Bartušek
Zdeněk Pospı́šil
Štefan Schwabik
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+
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Comparison results for solutions of time scale matrix Riccati equations and inequalities
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2006
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Roman Šimon Hilscher
Román
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+
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Comparison results for solutions of time scale matrix Riccatiequations and inequalities
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2006
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Roman Šimon Hilscher
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Riccati inequality and other results for discrete symplectic systems
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2005
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Roman Šimon Hilscher
Viera Štoudková Růžičková
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+
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SOLVABILITY OF THE DISCRETE LQR-PROBLEM UNDER MINIMAL ASSUMPTIONS
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2005
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Roman Šimon Hilscher
Vera Zeidan
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+
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Nonnegativity and positivity of quadratic functionals in discrete calculus of variations: survey
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2005
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Roman Šimon Hilscher
Vera Zeidan
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+
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AN EIGENVALUE PROBLEM FOR LINEAR HAMILTONIAN DYNAMIC SYSTEMS
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2005
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Martin Böhner
Roman Šimon Hilscher
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+
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Discrete Quadratic Functionals with Jointly Varying Endpoints via Separable Endpoints
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2004
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Roman Šimon Hilscher
Vera Zeidan
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+
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Equivalent conditions to the nonnegativity of a quadratic functional in discrete optimal control
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2004
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Roman Šimon Hilscher
Vera Zeidan
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PDF
Chat
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A Remark on Discrete Quadratic Functionals with Separable Endpoints
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2003
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Roman Šimon Hilscher
Vera Zeidan
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Coupled Intervals in the Discrete Optimal Control
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2003
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Roman Šimon Hilscher
Vera Zeidan
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+
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Calculus of variations on time scales: weak local piecewise Crd1 solutions with variable endpoints
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2003
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Roman Šimon Hilscher
Vera Zeidan
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+
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Nonnegativity of discrete quadratic functionals corresponding to symplectic difference systems
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2003
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Ondřej Došlý
Roman Šimon Hilscher
Vera Zeidan
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+
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Symplectic difference systems: variable stepsize discretization and discrete quadratic functionals
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2003
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Roman Šimon Hilscher
Vera Zeidan
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+
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A class of Sturm-Liouville difference equations: (Non)oscillation constants and property BD
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2003
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Ondřej Došlý
Roman Šimon Hilscher
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+
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Nonnegativity of a discrete quadratic functional in terms of the (strengthened) legendre and jacobi conditions
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2003
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Roman Šimon Hilscher
Vera Zeidan
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+
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RICCATI INEQUALITY, DISCONJUGACY, AND RECIPROCITY PRINCIPLE FOR LINEAR HAMILTONIAN DYNAMIC SYSTEMS
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2003
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Roman Šimon Hilscher
P. Řehák
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Symplectic Dynamic Systems
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2003
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Ondřej Došlý
Stefan Hilger
Roman Šimon Hilscher
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+
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DIAGONALIZATION APPROACH TO DISCRETE QUADRATIC FUNCTIONALS
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2003
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Martin Böhner
Ondřej Došlý
Werner Kratz
Roman Šimon Hilscher
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Coupled intervals in the discrete calculus of variations: necessity and sufficiency
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2002
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Roman Šimon Hilscher
Vera Zeidan
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+
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A time scales version of a Wirtinger-type inequality and applications
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2002
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Roman Šimon Hilscher
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Second Order Sufficiency Criteria for a Discrete Optimal Control Problem
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2002
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Roman Šimon Hilscher
Vera Zeidan
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+
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Discrete Optimal Control: Second Order Optimality Conditions
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2002
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Roman Šimon Hilscher
Vera Zeidan
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+
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Diagonalization approach to discrete quadratic functionals
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2002
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Werner Kratz
Matthias U. Bohner
Ondřej Došlý
Roman Šimon Hilscher
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+
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A time scales version of a Wirtinger type inequality and applications
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2002
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Roman Šimon Hilscher
Román
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+
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Linear Hamiltonian dynamic systems on time scales: Sturmian property of the principal solution
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2001
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Martin Böhner
O. Doš
Roman Šimon Hilscher
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+
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Discrete spectra criteria for certain classes of singular differential and difference operators
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2001
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Roman Šimon Hilscher
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Positivity of Quadratic Functionals on Time Scales: Necessity
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2001
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Roman Šimon Hilscher
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None
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2001
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Roman Šimon Hilscher
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+
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Reid Roundabout Theorem for Symplectic Dynamic Systems on Time Scales
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2001
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Roman Šimon Hilscher
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+
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Disconjugacy, transformations and quadratic functionals for symplectic dynamic systems on time scales
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2001
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Ondřrej Dořlý
Roman Šimon Hilscher
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+
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Inhomogeneous Quadratic Functionals on Time Scales
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2001
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Roman Šimon Hilscher
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+
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Inhomogeneous quadratic functionals on time scales
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2001
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Roman Šimon Hilscher
Román
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+
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Discrete spectra criteria for certain classes of singular diffferential and difference operators
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2001
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Roman Šimon Hilscher
Román
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+
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Linear Hamiltonian systems on time scales: Positivity of quadratic functionals
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2000
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Roman Šimon Hilscher
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Discrete Optimal Control: The Accessory Problem and Necessary Optimality Conditions
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2000
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Roman Šimon Hilscher
Vera Zeidan
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+
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On disconjugacy for vector linear Hamiltonian systems on time scales
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2000
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Roman Šimon Hilscher
Román
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+
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Spectral properties of general self-adjoint, even order differential operators
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2000
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Roman Šimon Hilscher
Román
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+
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Spectral properties of general self-adjoint, even orderdifferential operators
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2000
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Roman Šimon Hilscher
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+
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Linear Hamiltonian systems on time scales: positivity of quadratic functionals
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2000
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Roman Šimon Hilscher
Román
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+
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On disconjugacy for vector linear Hamiltonian systems on timescales
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2000
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Roman Šimon Hilscher
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PDF
Chat
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Disconjugacy of Symplectic Systems and Positive Definiteness of Block Tridiagonal Matrices
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1999
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Roman Šimon Hilscher
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+
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Linear Hamiltonian difference systems: Transformations, recessive solutions, generalized reciprocity
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1999
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Ondřej Došlý
Roman Šimon Hilscher
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+
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Disconjugacy of symplectic systems and positive definiteness of block tridiagonal matrices
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1999
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Roman Šimon Hilscher
Román
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+
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Linear Hamiltonian systems on time scales: transformations
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1999
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Roman Šimon Hilscher
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+
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Linear Hamiltonian systems on time scales: transformations
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1999
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Roman Šimon Hilscher
Román
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PDF
Chat
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Spectral properties of fourth order differential operators
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1997
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Ondřej Došlý
Roman Šimon Hilscher
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