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Sum of a second derivative operator with periodic boundary conditions and an integral operator of rank one (non-local potential) is studied in this manuscript. Not only spectral analysis is conducted for this operator but the inverse…

Functional Analysis · Mathematics 2020-01-17 Vladimir A. Zolotarev

A kinetic equation for Compton scattering is given that differs from the Kompaneets equation in several significant ways. By using an inverse differential operator this equation allows treatment of problems for which the radiation field…

Astrophysics · Physics 2009-11-07 George B. Rybicki

For a second-order strongly elliptic differential operator on an exterior domain in R^n it is known from works of Birman and Solomiak that a change of the boundary condition from the Dirichlet condition to an elliptic Neumann or Robin…

Analysis of PDEs · Mathematics 2011-03-02 Gerd Grubb

We analyze the inverse problem to reconstruct the shape of a three dimensional homogeneous dielectric obstacle from the knowledge of noisy far field data. The forward problem is solved by a system of second kind boundary integral equations.…

Numerical Analysis · Mathematics 2020-06-22 Thorsten Hohage , Frédérique Le Louër

We consider a quadratic matrix boundary value problem with equations and boundary conditions dependent on a spectral parameter. We study an inverse problem that consists in recovering the differential pencil by the so-called Weyl matrix. We…

Spectral Theory · Mathematics 2013-01-15 Natalia Bondarenko

This article is concerned with uniqueness and stability issues for the inverse spectral problem of recovering the magnetic field and the electric potential in a Riemannian manifold from some asymptotic knowledge of the boundary spectral…

Analysis of PDEs · Mathematics 2018-10-30 Mourad Bellassoued , Mourad Choulli , Dos Santos Ferreira , Yavar Kian , Plamen Stefanov

Many problems of applied mathematics are reduced to the solution of integral equations with special functions in kernels, therefore the inversion formulas for such equations play an important role in solving boundary value problems for…

Analysis of PDEs · Mathematics 2018-03-06 Tuhtasin Ergashev

We study an inverse problem involving the unique recovery of several lower order anisotropic tensor perturbations of a polyharmonic operator in a bounded domain from the knowledge of the Dirichlet to Neumann map on a part of boundary. The…

Analysis of PDEs · Mathematics 2021-11-16 Sombuddha Bhattacharyya , Venkateswaran P. Krishnan , Suman Kumar Sahoo

The paper deals with nonlocal differential operators possessing a term with frozen (fixed) argument appearing, in particular, in modelling various physical systems with feedback. The presence of a feedback means that the external affect on…

Spectral Theory · Mathematics 2021-03-16 Sergey Buterin , Yi-Teng Hu

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 paper, we consider Barcilon's inverse problem, which consists of the recovery of the fourth-order differential operator from three spectra. We obtain the relationship of Barcilon's three spectra with the Weyl-Yurko matrix. Moreover,…

Spectral Theory · Mathematics 2023-04-13 Aiwei Guan , Chuanfu Yang , Natalia P. Bondarenko

In this note, we solve an inverse spectral problem for a class of finite band symmetric matrices. We provide necessary and sufficient conditions for a matrix valued function to be a spectral function of the operator corresponding to a…

Mathematical Physics · Physics 2017-11-02 Mikhail Kudryavtsev , Sergio Palafox , Luis O. Silva

We consider an inverse spectral problem for a class of singular AKNS operators $H\_a, a\in\N$ with an explicit singularity. We construct for each $a\in\N$, a standard map $\lambda^a\times\kappa^a$ with spectral data $\lambda^a$ and some…

Spectral Theory · Mathematics 2016-08-16 Frédéric Serier

We consider the Schrodinger operator in n-dimensional rectangular domains with either Dirichlet or Neumann boundary conditions on the faces and study the constraints on the potential imposed by fixing the spectrum of the operator.We study…

Analysis of PDEs · Mathematics 2015-07-21 Gregory Eskin , James Ralston

We solve the inverse spectral problem of recovering the singular potentials $q\in W^{-1}_{2}(0,1)$ of Sturm-Liouville operators by two spectra. The reconstruction algorithm is presented and necessary and sufficient conditions on two…

Spectral Theory · Mathematics 2007-05-23 R. O. Hryniv , Ya. V. Mykytyuk

This work studies the inverse boundary problem for the two photon absorption radiative transport equation. We show that the absorption coefficients and scattering coefficients can be uniquely determined from the \emph{albedo} operator. If…

Analysis of PDEs · Mathematics 2022-02-21 Plamen Stefanov , Yimin Zhong

This paper explores the complexity associated with solving the inverse Sturm-Liouville problem with Robin boundary conditions: given a sequence of eigenvalues and a sequence of norming constants, how many limits does a universal algorithm…

Numerical Analysis · Mathematics 2023-12-27 Jonathan Ben-Artzi , Marco Marletta , Frank Rösler

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

We consider a Sturm-Liouville operator on a finite interval as well as a scattering problem on the real line both with transfer conditions at the origin. On a finite interval we show that the the Titchmarsh-Weyl $m$-function can be uniquely…

Spectral Theory · Mathematics 2018-04-20 Sonja Currie , Marlena Nowaczyk , Bruce A. Watson

In this paper, the existence of smooth positive solutions to a Robin boundary-value problem with non-homogeneous differential operator and reaction given by a nonlinear convection term plus a singular one is established. Proofs chiefly…

Analysis of PDEs · Mathematics 2019-09-24 Umberto Guarnotta , Salvatore A. Marano , Dumitru Motreanu