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We consider semi-infinite Jacobi matrices with discrete spectrum. We prove that the Jacobi operator can be uniquely recovered from one spectrum and subsets of another spectrum and norming constants corresponding to the first spectrum. We…

Spectral Theory · Mathematics 2023-10-25 Burak Hatinoğlu

Inverse spectral problems for Sturm-Liouville operators with nonlocal boundary conditions are studied. As the main spectral characteristics we introduce the so-called Weyl-type function and two spectra, which are generalizations of the…

Spectral Theory · Mathematics 2014-10-09 Vjacheslav Yurko , Chuan-Fu Yang

This paper is concerned with inverse spectral problems for higher-order ($n > 2$) ordinary differential operators. We develop an approach to the reconstruction from the spectral data for a wide range of differential operators with either…

Spectral Theory · Mathematics 2022-11-02 Natalia P. Bondarenko

Inverse problems for differential pencils with nonlocal conditions are investigated. Several uniqueness theorems of inverse problems from the Weyl-type function and spectra are proved, which are generalizations of the well-known Weyl…

Spectral Theory · Mathematics 2015-03-09 Chuan-Fu Yang , Vjacheslav Yurko

The matrix Sturm-Liouville operator with an integrable potential on the half-line is considered. We study the inverse spectral problem, which consists in recovering of this operator by the Weyl matrix. The main result of the paper is the…

Spectral Theory · Mathematics 2014-12-19 Natalia Bondarenko

This note deals with the direct and inverse spectral analysis for a class of infinite band symmetric matrices. This class corresponds to operators arising from difference quations with usual and inner boundary conditions. We give a…

Mathematical Physics · Physics 2015-12-02 Mikhail Kudryavtsev , Sergio Palafox , Luis O. Silva

In this paper, we for the first time get constructive solution for the inverse Sturm-Liouville problem with complex-valued singular potential and with polynomials of the spectral parameter in the boundary conditions. The uniqueness of…

Spectral Theory · Mathematics 2023-09-11 Egor E. Chitorkin , Natalia P. Bondarenko

Variable order differential equations with non-integrable singularities are considered on spatial networks. Properties of the spectrum are established, and the solution of the inverse spectral problem is obtained.

Spectral Theory · Mathematics 2015-07-03 Vjacheslav Yurko

Inverse problem to recover the skew-self-adjoint Dirac-type system from the generalized Weyl matrix function is treated in the paper. Sufficient conditions under which the unique solution of the inverse problem exists, are formulated in…

Classical Analysis and ODEs · Mathematics 2010-02-02 B. Fritzsche , B. Kirstein , A. L. Sakhnovich

The operator of double differentiation on a finite interval with Robin boundary conditions perturbed by the composition of a Volterra convolution operator and the differentiation one is considered. We study the inverse problem of recovering…

Spectral Theory · Mathematics 2020-01-28 S. A. Buterin , A. E. Choque Rivero

The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the…

Analysis of PDEs · Mathematics 2026-04-09 Rahul Bhardwaj , Manmohan Vashisth

We give a short review of results on inverse spectral problems for ordinary differential operators on a spatial networks (geometrical graphs). We pay the main attention to the most important nonlinear inverse problems of recovering…

Spectral Theory · Mathematics 2015-10-02 Vjacheslav Yurko

New formulas on the inverse problem for the continuous skew-self-adjoint Dirac type system are obtained. For the discrete skew-self-adjoint Dirac type system the solution of a general type inverse spectral problem is also derived in terms…

Spectral Theory · Mathematics 2007-05-23 Alexander Sakhnovich

The principal purpose of this note is to provide a reconstruction procedure for distributional matrix-valued potential coefficients of Schr\"odinger-type operators on a half-line from the underlying Weyl-Titchmarsh function.

Spectral Theory · Mathematics 2015-03-23 Jonathan Eckhardt , Fritz Gesztesy , Roger Nichols , Alexander Sakhnovich , Gerald Teschl

In this paper, we develop two approaches to investigation of inverse spectral problems for a new class of nonlocal operators on metric graphs. The Laplace differential operator is considered on a star-shaped graph with nonlocal integral…

Spectral Theory · Mathematics 2022-11-02 Natalia P. Bondarenko

We solve an inverse problem for a third order differential operator under the 3-point Dirichlet conditions. The third-order operator is an $L$-operator in the Lax pair for the good Boussinesq equation. We construct the mapping from the set…

Mathematical Physics · Physics 2024-08-06 Andrey Badanin , Evgeny Korotyaev

Inverse spectral problems are studied for the second order integro-differential operators on a finite interval. Properties of spectral characteristic are established, and the uniqueness theorem is proved for this class of inverse problems.

Spectral Theory · Mathematics 2017-02-06 Vjacheslav Yurko

In this paper, we for the first time prove local solvability and stability of an inverse spectral problem for higher-order ($n > 3$) differential operators with distribution coefficients. The inverse problem consists in the recovery of…

Spectral Theory · Mathematics 2023-09-11 Natalia P. Bondarenko

The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary…

Spectral Theory · Mathematics 2014-07-15 Natalia Bondarenko

We consider inverse dynamic and spectral problems for the one dimensional Dirac system on a finite tree. Our aim will be to recover the topology of a tree (lengths and connectivity of edges) as well as matrix potentials on each edge. As…

Spectral Theory · Mathematics 2019-12-19 A. S. Mikhaylov , V. S. Mikhaylov , G. E. Murzabekova