Perturbations of orthogonal polynomials with periodic recursion coefficients

David Damanik, Rowan Killip, Barry Simon

Type: Article

Publication Date: 2010-04-25

Citations: 116

DOI: https://doi.org/10.4007/annals.2010.171.1931

Abstract

The results of Denisov-Rakhmanov, Szegő-Shohat-Nevai, and Killip-Simon are extended from asymptotically constant orthogonal polynomials on the real line (OPRL) and unit circle (OPUC) to asymptotically periodic OPRL and OPUC.The key tool is a characterization of the isospectral torus that is well adapted to the study of perturbations.

Locations

arXiv (Cornell University) - View - PDF
Annals of Mathematics - View - PDF

Similar Works

Action	Title	Year	Authors
+	Perturbations of Orthogonal Polynomials With Periodic Recursion Coefficients	2007	David Damanik Rowan Killip Barry Simon
+	Perturbations of Orthogonal Polynomials With Periodic Recursion Coefficients	2007	David Damanik Rowan Killip Barry Simon
+	Finite perturbations of orthogonal polynomials	1992	Franz Peherstorfer
+ PDF Chat	Rearrangements of periodic multiplicative orthogonal series	1990	С. В. Бочкарев
+	Zeros of Orthogonal Polynomials Generated by Canonical Perturbations on Standard Measure	2010	Edmundo J. Huertas Francisco Marcellán Fernando R. Rafaeli
+ PDF Chat	Rank one perturbations and the zeros of paraorthogonal polynomials on the unit circle	2006	Barry Simon
+	Rank one perturbations and the zeros of paraorthogonal polynomials on the unit circle	2006	Barry Simon
+	Zeros of orthogonal polynomials generated by canonical perturbations of measures	2012	Edmundo J. Huertas Francisco Marcellán Fernando R. Rafaeli
+	Chain sequences and compact perturbations of orthogonal polynomials	1994	Ryszard Szwarc
+	From Random Matrices to Quasiperiodic Jacobi Matrices via Orthogonal Polynomials	2005	L. А. Pastur
+ PDF Chat	Oscillatory behavior of orthogonal polynomials	2019	Вилмос Тотик
+ PDF Chat	Oscillatory Behavior of Orthogonal Polynomials	1986	Attila Máté Paul Nevai Вилмос Тотик
+	Lacunary Orthogonal Polynomials	1966	H. van Rossum
+	Regular behavior of orthogonal polynomials and its localization	1991	Вилмос Тотик
+	Spectra of periodic operator polynomials with finitely many diagonals	2005	А. А. Панков Leiba Rodman
+	Orthogonal Polynomials on the Unit Circle	2005	Barry Simon
+	Orthogonal Polynomials on the Unit Circle	2005	Barry Simon
+	Orthogonal polynomials on the unit circle: Steklov problems and weight perturbations	2016	Keith Rush
+	Orthogonal polynomials on the unit circle	2008	Sergey Khrushchev
+	Polynomials orthogonal on the unit circle	1939	G. SzegÅ

Works That Cite This (119)

Action	Title	Year	Authors
+ PDF Chat	Spectra of Jacobi Operators via Connection Coefficient Matrices	2021	Marcus Webb Sheehan Olver
+ PDF Chat	Finite-Gap CMV Matrices: Periodic Coordinates and a Magic Formula	2019	Jacob S. Christiansen Benjamin Eichinger Tom VandenBoom
+ PDF Chat	Orthogonal Polynomials Associated with Equilibrium Measures on ℝ $\mathbb {R}$	2016	Gökalp Alpan
+ PDF Chat	Eigenvalue Bounds for Perturbations of Schrödinger Operators and Jacobi Matrices With Regular Ground States	2008	Rupert L. Frank Barry Simon Timo Weidl
+	Central Limit Theorems for Biorthogonal Ensembles and Asymptotics of Recurrence Coefficients	2013	Jonathan Breuer Maurice Duits
+	Kotani-Last problem and Hardy spaces on surfaces of Widom type	2012	Alexander Volberg Peter Yuditskii
+	Reflectionless Herglotz functions and generalized Lyapunov exponents	2008	Alexei Poltoratski Christian Remling
+ PDF Chat	Characteristic Polynomials of Random Banded Hessenberg Matrices and Hermite–Padé Approximation	2021	A. López‐García В. А. Прохоров
+ PDF Chat	On a Seminal Paper by Karlin and McGregor	2013	M. M. Castro F. Alberto Grünbaum
+ PDF Chat	Large deviations and sum rules for spectral theory: a pedagogical approach	2018	Jonathan Breuer Barry Simon Ofer Zeitouni

Works Cited by This (101)

Action	Title	Year	Authors
+	Orthogonal Polynomials, Recurrences, Jacobi Matrices, and Measures	1992	Paul Nevai
+ PDF Chat	Jacobi Operators and Completely Integrable Nonlinear Lattices	1999	Gerald Teschl
+	Orthogonal matrix polynomials with respect to linear matrix moment functionals: Theory and applications	1996	L. Jódar Emilio Defez E. Ponsoda
+ PDF Chat	Beiträge zur Theorie der Toeplitzschen Formen	1920	G. Szegö
+	Schur's Algorithm and Several Applications	1992	Mihály Bakonyi T. Constantinescu
+	Sturm-Liouville Operators and Applications	1986	V. А. Marchenko
+	On Rakhmanov’s theorem for Jacobi matrices	2003	Sergey A. Denisov
+	Realization Theorems for Operator-Valued R-Functions	1997	Sergey Belyi Eduard Tsekanovskiı̆
+	Methods of Modern Mathematical Physics	1972	Michael C. Reed Barry Simon
+ PDF Chat	Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum	1999	Fritz Gesztesy Barry Simon