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In this paper, we study the direct and inverse spectral problems for the Schrodinger operator with two generalized Regge boundary conditions. For the direct problem, we give the properties of the spectrum, including the asymptotic…

Spectral Theory · Mathematics 2025-08-22 Xiao-Chuan Xu , Yu-Ting Huang

We consider the inverse problem of the reconstruction of a Schr\"odinger operator on a unknown Riemannian manifold or a domain of Euclidean space. The data used is a part of the boundary $\Gamma$ and the eigenvalues corresponding to a set…

Analysis of PDEs · Mathematics 2009-11-10 Yaroslav Kurylev , Matti Lassas , Ricardo Weder

We consider inverse boundary value problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity…

Analysis of PDEs · Mathematics 2025-03-27 R. M. Brown , L. D. Gauthier

First order integro-differential operators on a finite interval are studied. Properties of spectral characteristic are established, and the uniqueness theorem is proved for the inverse problem of recovering operators from their spectral…

Spectral Theory · Mathematics 2017-05-17 Vjacheslav Yurko

In this article, we study the one-dimensional inverse problem of determining the memory kernel by the integral overdetermination condition for the direct problem of finding the velocity potential and the displacement of boundary points. A…

Analysis of PDEs · Mathematics 2026-02-24 Zhanna D. Totieva , Kush Kinra , Manil T. Mohan

The inverse spectral problem is studied for the Sturm-Liouville operator with a complex-valued potential and arbitrary entire functions in one of the boundary conditions. We obtain necessary and sufficient conditions for uniqueness, and…

Spectral Theory · Mathematics 2021-09-01 Natalia Bondarenko

We introduce a variational algorithm, which solves the classical inverse Sturm-Liouville problem when two spectra are given. In contrast to other approaches, it recovers the potential as well as the boundary conditions without a priori…

Numerical Analysis · Mathematics 2009-09-29 Norbert Roehrl

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

In this work, a complete solution of the inverse spectral problem for a class of Dirac differential equations system is given by spectral data (eigenvalues and normalizing numbers). As a direct problem, the eigenvalue problem is solved: the…

Spectral Theory · Mathematics 2015-10-13 Khanlar R. Mamedov , Ozge Akcay

In this paper, Dirac operator with some integral type nonlocal boundary conditions is studied. We show that the coefficients of the problem can be uniquely determined by a dense set of nodal points. Moreover, we give an algorithm for the…

Classical Analysis and ODEs · Mathematics 2022-08-04 A. Sinan Ozkan , İbrahim Adalar

In the paper, we study an inverse spectral problem for quadratic pencils of the Sturm--Liouville operators with singular coefficients and entire functions in the boundary conditions. We prove that a subspectrum is sufficient for recovering…

Spectral Theory · Mathematics 2022-04-26 Maria Kuznetsova

We study the inverse spectral problems of recovering Dirac-type functional-differential operator with two constant delays $a_1$ and $a_2$ not less than one-third of the interval. It has been proved that the operator can be recovered…

Spectral Theory · Mathematics 2023-08-17 Biljana Vojvodić , Nebojša Djurić , Vladimir Vladičić

As is known, for each fixed $\nu\in\{0,1\},$ the spectra of two operators generated by $-y''(x)+q(x)y(x-a)$ and the boundary conditions $y^{(\nu)}(0)=y^{(j)}(\pi)=0,$ $j=0,1,$ uniquely determine the complex-valued square-integrable…

Spectral Theory · Mathematics 2021-01-22 Nebojša Djurić , Sergey Buterin

Necessary and sufficient conditions are presented for a measure to be the spectral measure of a finite range or exponentially decaying perturbation of a periodic Jacobi operator. As a corollary we can fully solve the inverse resonance…

Classical Analysis and ODEs · Mathematics 2014-09-23 Rostyslav Kozhan

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

This paper deals with the Sturm-Liouville problem that feature distribution potential, polynomial dependence on the spectral parameter in the first boundary condition, and analytical dependence, in the second one. We study an inverse…

Spectral Theory · Mathematics 2024-09-05 E. E. Chitorkin , N. P. Bondarenko

We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray…

Analysis of PDEs · Mathematics 2020-02-24 Lauri Oksanen , Mikko Salo , Plamen Stefanov , Gunther Uhlmann

The Schroedinger equation on the half line is considered with a real-valued, integrable potential having a finite first moment. It is shown that the potential and the boundary conditions are uniquely determined by the data containing the…

Mathematical Physics · Physics 2009-11-10 Tuncay Aktosun , Ricardo Weder

Necessary and sufficient conditions are presented for a measure to be the spectral measure of a finite range perturbation of a Jacobi or CMV operator from a finite gap isospectral torus. The special case of eventually periodic operators…

Mathematical Physics · Physics 2016-06-22 Rostyslav Kozhan

Let $L_0$ be a closed densely defined symmetric semi-bounded operator with nonzero defect indexes in a separable Hilbert space ${\cal H}$. With $L_0$ we associate a metric space $\Omega_{L_0}$ that is named a {\it wave spectrum} and…

Functional Analysis · Mathematics 2010-04-13 M. I. Belishev