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We consider Sturm-Liouville operators on geometrical graphs without cycles (trees) with singular potentials from the class $W_2^{-1}$. We suppose that the potentials are known on a part of the graph, and study the so-called partial inverse…

Spectral Theory · Mathematics 2017-11-16 Natalia P. Bondarenko

We study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from their Dirichlet spectra and sequences of the norming constants. For the class of problems under consideration, we give a complete…

Spectral Theory · Mathematics 2015-06-04 Rostyslav Hryniv , Nataliya Pronska

We establish various uniqueness results for inverse spectral problems of Sturm-Liouville operators with a finite number of discontinuities at interior points at which we impose the usual transmission conditions. We consider both the case of…

Spectral Theory · Mathematics 2012-10-04 Mohammad Shahriari , Aliasghar Jodayree Akbarfam , Gerald Teschl

In recent years, there appeared a considerable interest in the inverse spectral theory for functional-differential operators with constant delay. In particular, it is well known that, for each fixed $\nu\in\{0,1\},$ the spectra of two…

Spectral Theory · Mathematics 2021-02-17 Nebojša Djurić , Sergey Buterin

In this paper, we develop a new approach to investigation of the uniform stability for inverse spectral problems. We consider the non-self-adjoint Sturm-Liouville problem that consists in the recovery of the potential and the parameters of…

Spectral Theory · Mathematics 2024-09-25 Natalia P. Bondarenko

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

Inverse spectral problems for Sturm-Liouville operators on a finite interval with non-separated boundary conditions are studied in the central symmetric case, when the potential is symmetric with respect to the middle of the interval. We…

Spectral Theory · Mathematics 2016-02-16 Vjacheslav Yurko

An inverse spectral problem is studied for the matrix Sturm-Liouville operator on a finite interval with the general self-adjoint boundary condition. We obtain a constructive solution based on the method of spectral mappings for the…

Spectral Theory · Mathematics 2020-03-05 Natalia Bondarenko

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

In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and…

Numerical Analysis · Mathematics 2015-06-04 Bangti Jin , William Rundell

We consider the inverse Sturm-Liouville problem with one discontinuous point on three-star graph, we deduced the distribution of the eigenvalues, and proved that one spectrum could uniquely determine the unknown potential and jump…

Spectral Theory · Mathematics 2020-12-30 Kang Lv

We consider two main inverse Sturm-Liouville problems: the problem of recovery of the potential and the boundary conditions from two spectra or from a spectral density function. A simple method for practical solution of such problems is…

Numerical Analysis · Mathematics 2021-02-03 Vladislav V. Kravchenko , Sergii M. Torba

The matrix Sturm-Liouville operator on a finite interval with the boundary conditions in the general self-adjoint form and with the singular potential from the class $W_2^{-1}$ is studied. This operator generalizes Sturm-Liouville operators…

Spectral Theory · Mathematics 2021-04-28 Natalia P. Bondarenko

In this paper, a Sturm-Liouville boundary value problem equiped with conformable fractional derivates is considered. We give some uniqueness theorems for the solutions of inverse problems according to the Weyl function, two given spectra…

Classical Analysis and ODEs · Mathematics 2022-03-23 A. Sinan Ozkan , İbrahim Adalar

We solve the inverse spectral problems for the class of Sturm--Liouville operators with singular real-valued potentials from the Sobolev space W^{s-1}_2(0,1), s\in[0,1]. The potential is recovered from two spectra or from the spectrum and…

Functional Analysis · Mathematics 2007-05-23 R. O. Hryniv , Ya. V. Mykytyuk

The paper deals with two inverse problems for Sturm--Liouville operator $Ly=-y" +q(x)y$ on the finite interval $[0,\pi]$. The first one is the problem of recovering of a potential by two spectra. We associate with this problem the map $F:\,…

Spectral Theory · Mathematics 2010-10-29 A. M. Savchuk , A. A. Shkalikov

The Sturm-Liouville operator with singular potentials on the lasso graph is considered. We suppose that the potential is known a priori on the boundary edge, and recover the potential on the loop from a part of the spectrum and some…

Spectral Theory · Mathematics 2017-11-16 Chuan-Fu Yang , Natalia P. Bondarenko

We consider the spectral problems for the Sturm-Liouville operator generated by the Dirichlet, Neumann, Dirichlet-Neumann and Neumann-Dirichlet conditions. The necessary and sufficient condition for the coincidence of the spectrum of the…

Functional Analysis · Mathematics 2019-12-30 B. N. Biyarov

In a finite-dimensional Euclidian space we consider a connected metric graph with the following property: each two cycles can have at most one common point. Such graphs are called A-graphs. On noncompact A-graph we consider a scattering…

Spectral Theory · Mathematics 2013-11-13 Mikhail Ignatyev

Solving inverse scattering problem for a discrete Sturm-Liouville operator with the fast decreasing potential one gets reflection coefficients $s_\pm$ and invertible operators $I+H_{s_\pm}$, where $ H_{s_\pm}$ is the Hankel operator related…

Spectral Theory · Mathematics 2009-11-07 A. Volberg , P. Yuditskii