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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

This article is concerned with an inverse problem of simultaneously determining a spatially varying coefficient and a Robin coefficient for a one-dimensional fractional diffusion equation with a time-fractional derivative of order…

Analysis of PDEs · Mathematics 2024-10-23 Xiaohua Jing , Zhiyuan Li , Masahiro Yamamoto

This paper is devoted to the study of a partial inverse spectral problem for Sturm-Liouville operators with frozen arguments on a star-shaped graph. The potentials are assumed to be known a priori on all edges except one, and the objective…

Spectral Theory · Mathematics 2025-06-26 Chung-Tsun Shieh , Tzong-Mo Tsai , Meng-Nien Wu

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

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

We consider a Sturm--Liouville boundary value problem in a boun\-ded domain $\cD$ of $\mathbb{R}^n$. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in $\cD$ and the boundary…

Analysis of PDEs · Mathematics 2022-02-22 A. Shlapunov , N. Tarkhanov

In this paper, we study the inverse spectral problem for the Sturm-Liouville operators on a star-shaped graph, which consists in the recovery of the potentials from specral data or several spectra. The uniform stability of these inverse…

Spectral Theory · Mathematics 2026-01-16 E. E. Chitorkin , N. P. Bondarenko

In this paper, the Sturm-Liouville problem with nonseparated quasiperiodic boundary conditions is considered. We study the recovery of the problem parameters from the Hill-type discriminant, the Dirichlet spectrum, and the sequence of…

Spectral Theory · Mathematics 2025-07-29 Natalia P. Bondarenko

In this work, we study the inverse spectral problems for the Sturm-Liouville operators on [0,1] with complex coefficients and a discontinuity at $x=a\in(0,1)$. Assume that the potential on (a,1) and some parameters in the discontinuity and…

Spectral Theory · Mathematics 2025-08-22 Xiao-Chuan Xu , Chuan-Fu Yang , Natalia Pavlovna Bondarenko

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

The inverse problem of determining the order of the fractional Riemann- Liouville derivative with respect to time in the subdi_usion equation with an arbitrary positive self-adjoint operator having a discrete spectrum is considered. Using…

General Mathematics · Mathematics 2021-08-12 Shavkat Alimov , Ravshan Ashurov

We establish some relationships between an m-accretive operator and its Moore-Penorse inverse. We derive some perturbation result of the Moore-Penorse inverse of a maximal accretive operator. As an application we give a factorization…

Functional Analysis · Mathematics 2021-09-21 Fairouz Bouchelaghem , Mohammed Benharrat

We comparatively use some classical spectral collocation methods as well as highly performing Chebfun algorithms in order to compute the eigenpairs of second order singular Sturm-Liouville problems with separated self-adjoint boundary…

Numerical Analysis · Mathematics 2020-12-03 Calin-Ioan Gheorghiu

The inverse spectral theory for a self-adjoint one-dimensional Dirac operator associated periodic potentials is formulated via a Riemann-Hilbert problem approach. The resulting formalism is also used to solve the initial value problem for…

Analysis of PDEs · Mathematics 2026-01-12 Gino Biondini , Zechuan Zhang

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

In this work, we consider the Sturm-Liouville operator on a finite interval $[0,1]$ with discontinuous conditions at $1/2$. We prove that if the potential is known a priori on a subinterval $[b,1]$ with $b\ge1/2$, then parts of two spectra…

Spectral Theory · Mathematics 2017-03-07 Xiao-Chuan Xu , Chuan-Fu Yang

In this work, we investigate the existence of positive solutions for a multi-point boundary value problem for a second order delay differential equation. Under certain growth conditions on the nonlinearity, and by the mean of Leray-Schauder…

Analysis of PDEs · Mathematics 2018-01-09 Abdelkader Lakmeche , Horiya Habbaze , Ahmed Lakmeche

In this paper, we consider a discontinuous Dirac operator depending polynomially on the spectral parameter and a finite number of transmission conditions. We get some properties of eigenvalues and eigenfunctions. Then, we investigate some…

Classical Analysis and ODEs · Mathematics 2016-01-21 Yalçın Güldü , Merve Arslantaş

This article deals with a special case of the Sturm-Liouville boundary value problem (BVP), an eigenvalue problem characterized by the Sturm-Liouville differential operator with unknown spectra and the associated eigenfunctions. By…

Classical Analysis and ODEs · Mathematics 2022-02-02 N. Karjanto

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