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The author studies the inverse spectral problem of Sturm-Liouville operator on a star-like graph. To this star-like graph centered at the origin as its vertex, there are attached $m$ edges that imposed the Sturm-Liouville operator with…

Mathematical Physics · Physics 2025-06-30 Lung-Hui Chen

The main goal of this paper is to propose an approach to inverse spectral problems for functional-differential operators (FDO) with involution. For definiteness, we focus on the second-order FDO with involution-reflection. Our approach is…

Spectral Theory · Mathematics 2021-07-27 Natalia P. Bondarenko

In this study, the theorem on necessary and sufficient conditions for the solvability of inverse problem for Sturm-Liouville operator with discontinuous coefficient is proved and the algorithm of reconstruction of potential from spectral…

Spectral Theory · Mathematics 2016-04-21 Döne Karahan , Khanlar. R. Mamedov

In the present paper, motivated by point interaction, we propose a new and explicit approach to inverse Sturm-Liouville eigenvalue problems under Dirichlet boundary. More precisely, when a given Sturm-Liouville eigenvalue problem with the…

Spectral Theory · Mathematics 2024-07-25 Min Zhao , Jiangang Qi , Xiao Chen

We consider the non-self-adjoint Sturm-Liouville operator on a finite interval. The inverse spectral problem is studied, which consists in recovering this operator from its eigenvalues and generalized weight numbers. We prove local…

Spectral Theory · Mathematics 2020-02-13 Natalia P. Bondarenko

The limit distribution of the discrete spectrum of the Sturm-Liouville problem with complex-valued polynomial potential on an interval, on a half-axis, and on the entire axis is studied. It is shown that at large parameter values, the…

Spectral Theory · Mathematics 2016-04-20 A. A. Shkalikov , S. N. Tumanov

We consider Sturm-Liouville operators with singular potentials from the class on star-type graph with cycle, which consist the edges with commensurable lengths. Asymptotic representation for eigenvalues for such operators is obtained.…

Spectral Theory · Mathematics 2019-01-31 Sergey V. Vasilev

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

We study an inverse spectral problem for arbitrary order ordinary differential equations on compact star-type graphs when differential equations have regular singularities at boundary vertices. As the main spectral characteristics we…

Spectral Theory · Mathematics 2014-10-09 Vjacheslav Yurko

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

The inverse scattering problem for Sturm-Liouville operators on the line with a matrix transfer condition at the origin is considered. We show that the transfer matrix can be reconstructed from the eigenvalues and reflection coefficient. In…

Spectral Theory · Mathematics 2017-07-05 Sonja Currie , Marlena Nowaczyk , Bruce Alastair Watson

In the paper, we study the problem of recovering the potential from the spectrum of the Dirichlet boundary value problem for a Sturm--Liouville equation with frozen argument on a closed set. We consider the case when the closed set consists…

Spectral Theory · Mathematics 2024-04-12 Maria Kuznetsova

In this paper, the inverse Sturm-Liouville problem with distribution potential and with polynomials of the spectral parameter in one of the boundary conditions is considered. We for the first time prove local solvability and stability of…

Spectral Theory · Mathematics 2024-02-12 Egor E. Chitorkin , Natalia P. Bondarennko

In this work, a boundary value problem for Sturm-Liouville operator with discontinuous coefficient is examined. The main equation is obtained which has an important role in solution of inverse problem for boundary value problem and…

Classical Analysis and ODEs · Mathematics 2016-10-31 Khanlar R. Mamedov , Done Karahan

We consider the inverse problem for countable, locally finite electrical networks with edge weights in an arbitrary field. The electrical inverse problem seeks to determine the weights of the edges knowing only the potential and current…

Combinatorics · Mathematics 2016-05-31 David Jekel

We consider an inverse optimization spectral problem for the Sturm-Liouville operator $$\mathcal{L}[q] u:=-u''+q(x)u$$ subject to the separated boundary conditions. In the main result, we prove that this problem is related to the existence…

Analysis of PDEs · Mathematics 2018-09-05 Y. Sh. Ilyasov , N. F. Valeev

We suggest a new statement of the inverse spectral problem for Sturm--Liouville-type operators with constant delay. This inverse problem consists in recovering the coefficient (often referred to as potential) of the delayed term in the…

Spectral Theory · Mathematics 2023-04-13 Sergey Buterin , Sergey Vasilev

We consider a class of self-adjoint Sturm-Liouville problems with rational functions of the spectral parameter in the boundary conditions. The uniform stability for direct and inverse spectral problems is proved for the first time for…

Spectral Theory · Mathematics 2025-09-03 Natalia P. Bondarenko

We study the inverse Sturm-Liouville problem on a finite interval from partial knowledge of spectral data. Specifically, we show that the potential can be uniquely reconstructed from the knowledge of a fraction of Dirichlet eigenvalues…

Analysis of PDEs · Mathematics 2026-03-30 Ali Feizmohammadi , Yavar Kian

In this paper, the uniform stability of the inverse spectral problem is proved for the matrix Sturm-Liouville operator on a finite interval. Namely, we describe the sets of spectral data, on which the inverse spectral mapping is bounded…

Spectral Theory · Mathematics 2026-02-17 Natalia P. Bondarenko