English
Related papers

Related papers: Partial Information for Inverse Spectral Uniquenes…

200 papers

This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at subboundary. Uniqueness result is obtained by using the…

Analysis of PDEs · Mathematics 2021-12-08 Xing Cheng , Zhiyuan Li

We give a short review of results on inverse spectral problems for ordinary differential operators on a spatial networks (geometrical graphs). We pay the main attention to the most important nonlinear inverse problems of recovering…

Spectral Theory · Mathematics 2015-10-02 Vjacheslav Yurko

We study an inverse problem for fractional elasticity. In analogy to the classical problem of linear elasticity, we consider the unique recovery of the Lam\'e parameters associated to a linear, isotropic fractional elasticity operator from…

Analysis of PDEs · Mathematics 2022-10-03 Giovanni Covi , Maarten de Hoop , Mikko Salo

We utilize the theory of de Branges spaces to show when certain Schr\"odinger operators with strongly singular potentials are uniquely determined by their associated spectral measure. The results are applied to obtain an inverse uniqueness…

Spectral Theory · Mathematics 2014-01-14 Jonathan Eckhardt

An overview of the authors results is given. Property C for ODE is defioned, It is proved that the pair of Sturm-Liouville operators has property C. This property is applied to many inverse problems. Some well-known results, such as…

Mathematical Physics · Physics 2007-05-23 Alexander G. Ramm

Spectral asymptotics of the Sturm-Liouville problem with an arithmetically self-similar singular weight is considered. Previous results by A. A. Vladimirov and I. A. Sheipak, and also by the author, rely on the spectral periodicity…

Spectral Theory · Mathematics 2023-05-30 N. V. Rastegaev

Inverse spectral problems are studied for first-order integro-differential operators on a finite interval. These problems consist in recovering some components of the kernel from one or multiple spectra. Uniqueness theorems are proved for…

Spectral Theory · Mathematics 2019-11-25 Natalia Bondarenko , Vjacheslav Yurko

Let $\Omega =\omega\times\mathbb R$ where $\omega\subset \mathbb R^2$ be a bounded domain, and $V : \Omega \to\mathbb R$ a bounded potential which is $2\pi$-periodic in the variable $x_{3}\in \mathbb R$. We study the inverse problem…

Analysis of PDEs · Mathematics 2016-02-01 Otared Kavian , Yavar Kian , Eric Soccorsi

This paper revisits the classical problem "Can we hear the density of a string?", which can be formulated as an inverse spectral problem for a Sturm-Liouville operator. Based on inverting a sequence of trace formulas, we propose a new…

Numerical Analysis · Mathematics 2019-07-01 Xiang Xu , Jian Zhai

An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…

Mathematical Physics · Physics 2007-05-23 A. G. Ramm

In this work we study the point spectra of selfadjoint Sturm-Liouville operators with generalized point interactions, where the two one-sided limits of the solution data are related via a general $\mathrm{SL}(2,\mathbb{R})$ matrix. We are…

Spectral Theory · Mathematics 2019-08-28 David Damanik , Rafael del Rio , Asaf L. Franco

Vibrations of an elastic rod are described by a Sturm-Liouville system. We present a general discussion of isospectral (spectrum preserving) deformations of such a system. We interpret one family of such deformations in terms of a…

Exactly Solvable and Integrable Systems · Physics 2019-12-30 Xiang-Ke Chang , Jacek Szmigielski

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

We consider the spectral problem generated by the Sturm-Liouville equation with an arbitrary complex-valued potential q(x) and irregular boundary conditions. We establish necessary and sufficient conditions for a set of complex numbers to…

Spectral Theory · Mathematics 2009-03-17 Alexander Makin

Spectral asymptotics of the Sturm-Liouville problem with a singular self-conformal weight measure is considered. A stronger version of the bounded distortion property is assumed for the conformal iterated function system corresponding to…

Spectral Theory · Mathematics 2017-11-07 U. R. Freiberg , N. V. Rastegaev

We study spectral subspaces of the Sturm-Liouville operator $f \mapsto -(pf')'$ on $\mathbb{R}$, where $p$ is a positive, piecewise constant function. Functions in these subspaces can be thought of as having a local bandwidth determined by…

Classical Analysis and ODEs · Mathematics 2024-05-21 Mark Jason Celiz , Karlheinz Gröchenig , Andreas Klotz

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

This paper is concerning the inverse conductive scattering of acoustic waves by a bounded inhomogeneous object with possibly embedded obstacles inside. A new uniqueness theorem is proved that the conductive object is uniquely determined by…

Analysis of PDEs · Mathematics 2026-01-19 Chengyu Wu , Jiaqing Yang

We study inverse spectral problems for ordinary differential equations with regular singularities on compact star-type graphs when differential equations have different orders on diferent edges. As the main spectral characteristics we…

Spectral Theory · Mathematics 2015-03-06 Vjacheslav Yurko

In this study, we give a regular fractional Sturm Liouville problem for diffusion operator (FSLPDO), research the spectral properties of the eigenfunctions and eigenvalues of the diffusion operator. We show that the eigenvalues and…

Spectral Theory · Mathematics 2013-11-07 Erdal Bas , Funda Metin