Inverse spectral problems and closed exponential systems

Miklós Horváth

Type: Article

Publication Date: 2005-09-01

Citations: 80

DOI: https://doi.org/10.4007/annals.2005.162.885

Abstract

Consider the inverse eigenvalue problem of the Schrödinger operator defined on a finite interval.We give optimal and almost optimal conditions for a set of eigenvalues to determine the Schrödinger operator.These conditions are simple closedness properties of the exponential system corresponding to the known eigenvalues.The statements contain nearly all former results of this topic.We give also conditions for recovering the Weyl-Titchmarsh m-function from its values m(λ n ).

Locations

Annals of Mathematics - View - PDF

Similar Works

Action	Title	Year	Authors
+	Inverse eigenvalue problems	2016	Miklós Horváth Orsolya Sáfár
+	Random inverse spectral problems and closed random exponential systems	2014	Xiangdong Yang
+	INVERSE EIGENVALUE PROBLEMS FOR SMOOTH POTENTIAL	2012	Orsolya Sáfár
+	Inverse spectral problems for radial Schrödinger operators and closed systems	2022	Xin-Jian Xu Chuan‐Fu Yang Natalia P. Bondarenko
+	Inverse eigenvalue problems.	1969	Thomas J. Cramton
+	Inverse problems for a Schrödinger-type equation	2008	Arif Amirov Masahiro Yamamoto
+	Inverse Problems for a Schrödinger-Type Equation	2008	Komaba Meguro
+ PDF Chat	Trace formulae and inverse spectral theory for Schrödinger operators	1993	Fritz Gesztesy Helge Holden Barry Simon Zhixue Zhao
+	INVERSE SPECTRAL THEORY	2004	Hiroshi Isozaki
+	Inverse Eigenvalue Problems	2005	Moody T. Chu Gene H. Golub
+	Inverse Scattering Theory	1998	Carlo Cercignani D. H. Sattinger
+	On the Inverse Resonance Problem for Schrödinger Operators	2009	Marco Marlettta Roman Shterenberg Rudi Weikard
+	Inverse spectral problems for Schrödinger and pseudo-differential operators	2013	Brice Camus
+ PDF Chat	Inverse Spectral Problems for Schrödinger Operators	2009	Hamid Hezari
+	Inverse Eigenvalue Problems for Complex Matrices	1970	G. N. de Oliveria
+	Inverse eigenvalue problems : theory and algorithms.	1998	Attalla Atia May Ramsis.
+	Stability of Direct and Inverse Eigenvalue Problems for Schrodinger Operators on Finite Intervals	2009	Miklós Horváth Márton Kiss
+	Inverse Eigenvalue Problems	2006	Alberto Borobia
+	Inverse Eigenvalue Problems	2013	Alberto Borobia
+	Inverse eigenvalue problems	1986	Victor Barcilon

Works That Cite This (77)

Action	Title	Year	Authors
+	Inverse spectral problems for the Sturm–Liouville operator with discontinuity	2016	Xiao‐Chuan Xu Chuan‐Fu Yang
+	On the uniqueness of inverse spectral problems associated with incomplete spectral data	2018	Zhaoying Wei Guangsheng Wei
+ PDF Chat	Inverse problems for a conformable fractional Sturm–Liouville operator	2020	İbrahi̇m Adalar A. Sinan Ozkan
+	An Ambarzumian type theorem on graphs with odd cycles	2023	Márton Kiss
+	Stability of direct and inverse eigenvalue problems: the case of complex potentials	2011	Miklós Horváth Márton Kiss
+	Inverse spectral problems for 2<i>m</i>-dimensional canonical Dirac operators	2007	Chuan‐Fu Yang Zhen-You Huang
+	Meromorphic Inner Functions, Toeplitz Kernels and the Uncertainty Principle	2006	Nikolai Makarov Alexei Poltoratski
+	Inverse Problems for Sturm–Liouville Equations with Boundary Conditions Linearly Dependent on the Spectral Parameter from Partial Information	2013	Wang Yu Ping Chung‐Tsun Shieh
+ PDF Chat	Reconstruction of the Sturm-Liouville operators on a graph with $\delta'_s$ couplings	2011	Chuan‐Fu Yang
+	Inverse spectral problems for radial Schrödinger operators and closed systems	2022	Xin-Jian Xu Chuan‐Fu Yang Natalia P. Bondarenko

Works Cited by This (12)

Action	Title	Year	Authors
+	An introduction to nonharmonic Fourier series	1980	Robert M. Young
+	Inverse scattering with fixed energy and an inverse eigenvalue problem on the half-line	2006	Miklós Horváth
+ PDF Chat	Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum	1999	Fritz Gesztesy Barry Simon
+	None	1997	Rafael del-Rio Fritz Gesztesy Barry Simon
+	A Proof of the Local Borg-Marchenko Theorem	2001	Christer Bennewitz
+	An Inverse Sturm–Liouville Problem with Mixed Given Data	1978	Harry Hochstadt Burton Lieberman
+ PDF Chat	A New Approach to Inverse Spectral Theory, II. General Real Potentials and the Connection to the Spectral Measure	2000	Fritz Gesztesy Barry Simon
+ PDF Chat	A New Approach to Inverse Spectral Theory, I. Fundamental Formalism	1999	Barry Simon
+	The Inverse Sturm-Liouville Problem	1998	Norman Levinson
+	Sturm-Liouville operators and their applications	1977	V. А. Marchenko