English
Related papers

Related papers: On a new inverse spectral problem

200 papers

We consider second-order functional differential operators with a constant delay. Properties of their spectral characteristics are obtained and a nonlinear inverse problem is studied, which consists in recovering the operators from their…

Spectral Theory · Mathematics 2018-02-08 Natalia Bondarenko , Vjacheslav Yurko

In this paper, the linear differential expression of order $n \ge 2$ with distribution coefficients of various singularity orders is considered. We obtain the associated matrix for the regularization of this expression. Furthermore, we…

Spectral Theory · Mathematics 2023-03-29 Natalia P. Bondarenko

The basic purpose of the present paper is the full solutions of the inverse problem (i.e. a finding of necessary and sufficient conditions) for the operator with complex periodic coefficients.

Spectral Theory · Mathematics 2007-05-23 Rakib Feyruz Efendiev

The stated paper is dedicated to one of the inverse problems of spectral theory. It is necessary to define matrix (constant) coefficients of some quadratic pencil, if the eigenvalues of this pencil are known. Furthermore, it is known that…

Spectral Theory · Mathematics 2015-12-02 N. A. Aliyev , Y. Y. Mustafayeva , R. F. Efendiyev

Boundary value problems on hedgehog-type graphs for Sturm-Liouville differential operators with general matching conditions are studied. We investigate inverse spectral problems of recovering the coefficients of the differential equation…

Spectral Theory · Mathematics 2015-02-02 Vjacheslav Yurko

In this paper, we consider a problem for the first order Dirac differential equations system with spectral parameter dependent in boundary condition. The asymptotic behaviors of eigenvalues, eigenfunctions and normalizing numbers of this…

Spectral Theory · Mathematics 2014-04-02 Kh. R. Mamedov , O. Akcay

In this paper, partial inverse problems for the quadratic pencil of Sturm-Liouville operators on a graph with a loop were studied. These problems consist in recovering the pencil coefficients on one edge of the graph (a boundary edge or the…

Spectral Theory · Mathematics 2020-05-12 Natalia P. Bondarenko , Chung-Tsun Shieh

In this work, we study the inverse spectral problem, using the Weyl matrix as the input data, for the matrix Schrodinger operator on the half-line with the boundary condition being the form of the most general self-adjoint. We prove the…

Spectral Theory · Mathematics 2024-11-12 Xiao-Chuan Xu , Yi-Jun Pan

We study Sturm--Liouville differential operators on the time scales consisting of a finite number of isolated points and segments. In a previous paper it was established that such operators are uniquely determined by their spectral…

Spectral Theory · Mathematics 2021-07-13 Maria Andreevna Kuznetsova

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 the inverse spectral problem for the third-order differential equation with distribution coefficient. The inverse problem consists in the recovery of the differential expression coefficients from the spectral…

Spectral Theory · Mathematics 2023-03-24 Natalia P. Bondarenko

The inverse spectral problem for the second-order differential pencil with quadratic dependence on the spectral parameter is studied. We obtain sufficient conditions for the global solvability of the inverse problem, prove its local…

Spectral Theory · Mathematics 2021-03-18 Natalia P. Bondarenko , Andrey V. Gaidel

We consider a pencil of non-self-adjoint matrix Sturm-Liouville operators on the half line and study the inverse problem of constructing this pencil by its Weyl matrix. A uniqueness theorem is proved, and a constructive algorithm for the…

Spectral Theory · Mathematics 2013-02-12 Natalia Bondarenko , Gerhard Freiling

A third order self-adjoint differential operator with periodic boundary conditions and an one-dimensional perturbation has been considered. For this operator, we first show that the spectrum consists of simple eigenvalues and finitely many…

Classical Analysis and ODEs · Mathematics 2022-12-21 Yixuan Liu , Jun Yan

In this work, we are concerned with inverse problems involving poly-fractional operators, where the poly-fractional operator is of the form \[P( (-\Delta_g)^s)u := \sum_{i=1}^M \alpha_i(-\Delta_{g_i})^{s_i}u\] for $s=(s_1,\dots,s_M)$,…

Analysis of PDEs · Mathematics 2025-05-14 Ching-Lung Lin , Hongyu Liu , Catharine W. K. Lo

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…

Spectral Theory · Mathematics 2013-03-22 David Andrew Smith , Beatrice Pelloni

Non-self-adjoint second-order ordinary differential operators on a finite interval with complex weights are studied. Properties of spectral characteristics are established and the inverse problem of recovering operators from their spectral…

Spectral Theory · Mathematics 2024-02-09 V. A. Yurko

In this study, singular diffusion operator with jump conditions is considered. Integral representations have been derived for solutions that satisfy boundary conditions and jump conditions. Some properties of eigenvalues and eigenfunctions…

Spectral Theory · Mathematics 2020-06-25 Abdullah Ergün

In this paper inverse problems for Dirac operator with nonlocal conditions are considered. Uniqueness theorems of inverse problems from the Weyl-type function and spectra are provided, which are generalizations of the well-known Weyl…

Spectral Theory · Mathematics 2015-03-06 Chuan-Fu Yang , Vjacheslav Yurko

Inverse spectral problems consist in recovering operators by their spectral characteristics. The problem of recovering the Sturm-Liouville operator with one frozen argument was studied earlier in works of various authors. In this paper, we…

Spectral Theory · Mathematics 2025-04-14 Maria Kuznetsova