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We examine inverse problems for the variable-coefficient nonlocal parabolic operator $(\partial_t - \Delta_g)^s$, where $0 < s < 1$. This article makes two primary contributions. First, we introduce a novel entanglement principle for these…

Analysis of PDEs · Mathematics 2025-10-22 Ru-Yu Lai , Yi-Hsuan Lin , Lili Yan

We study the non-selfadjoint Dirac system on a finite interval having non-integrable regular singularities in interior points with additional matching conditions at these points. Properties of spectral characteristics are established, and…

Spectral Theory · Mathematics 2015-02-02 Oleg Gorbunov , Vjacheslav Yurko

Scattering problem for a self-adjoint integro-differential operator, which is the sum of the operator of second derivative and of a finite-dimensional self-adjoint operator, is studied. Jost solutions are found and it is shown that the…

Classical Analysis and ODEs · Mathematics 2023-12-25 Vladimir A. Zolotarev

The inverse problem for the differential operator pencil with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator…

Spectral Theory · Mathematics 2010-03-30 R. F. Efendiev

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

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

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

In this paper, we study the spectral fractional Laplacian with inhomogeneous Dirichlet boundary data. Our contributions are twofold: first we introduce a Dirichlet-to-Neumann map for this operator and analyze an associated inverse problem;…

Analysis of PDEs · Mathematics 2026-04-09 Ravi Shankar Jaiswal , Pu-Zhao Kow , Suman Kumar Sahoo

This paper addresses inverse spectral problems associated with Dirac-type operators with a constant delay, specifically when this delay is less than one-third of the interval length. Our research focuses on eigenvalue behavior and operator…

Spectral Theory · Mathematics 2024-08-05 Nebojša Djurić , Biljana Vojvodić

In different branches of physics, we frequently deal with vector del operator ($\vec{\nabla}$). This del operator is generally used to find curl or divergence of a vector function or gradient of a scalar function. In many important cases,…

Mathematical Physics · Physics 2010-08-25 Shaon Sahoo

We consider an inverse problem for a higher order elliptic operator where the principal part is the polyharmonic operator $(-\Delta)^m$ with $ m \geq 2$. We show that the map from the coefficients to a certain bilinear form is injective. We…

Analysis of PDEs · Mathematics 2025-01-06 Russell M. Brown , Landon Gauthier , Daniel Faraco

Given a one-dimensional weighted Dirac operator we can define a spectral measure by virtue of singular Weyl-Titchmarsh-Kodaira theory. Using the theory of de Branges spaces we show that the spectral measure uniquely determines the Dirac…

Spectral Theory · Mathematics 2015-06-26 Jonathan Eckhardt , Aleksey Kostenko , Gerald Teschl

We study the inverse spectral problems of recovering Dirac-type functional-differential operator with two constant delays $a_1$ and $a_2$ not less than one-third of the interval. It has been proved that the operator can be recovered…

Spectral Theory · Mathematics 2023-08-17 Biljana Vojvodić , Nebojša Djurić , Vladimir Vladičić

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

Inverse problem for Dirac systems with locally square summable potentials and rectangular Weyl functions is solved. For that purpose we use a new result on the linear similarity between operators from a subclass of triangular integral…

Classical Analysis and ODEs · Mathematics 2016-11-03 Alexander Sakhnovich

The present paper plans to examine the existence, uniqueness and data dependence of the solution of the fractional functional differential equation with the abstract operator of Volterra, in the context of the Picard operators. We present…

Classical Analysis and ODEs · Mathematics 2018-11-06 J. Vanterler da C. Sousa , E. Capelas de Oliveira , Kishor D. Kucche

The spectral properties of Dirac operators on $(0,1)$ with potentials that belong entrywise to $L_p(0,1)$, for some $p\in[1,\infty)$, are studied. The algorithm of reconstruction of the potential from two spectra or from one spectrum and…

Spectral Theory · Mathematics 2007-05-23 S. Albeverio , R. Hryniv , Ya. Mykytyuk

We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray…

Analysis of PDEs · Mathematics 2020-02-24 Lauri Oksanen , Mikko Salo , Plamen Stefanov , Gunther Uhlmann

This paper is concerned with inverse spectral problems for higher-order ($n > 2$) ordinary differential operators. We develop an approach to the reconstruction from the spectral data for a wide range of differential operators with either…

Spectral Theory · Mathematics 2022-11-02 Natalia P. Bondarenko

We consider a Dirac-type operator $D_P$ on a vector bundle $V$ over a compact Riemannian manifold $(M,g)$ with a nonempty boundary. The operator $D_P$ is specified by a boundary condition $P(u|_{\p M})=0$ where $P$ is a projector which may…

Analysis of PDEs · Mathematics 2007-05-23 Yaroslav Kurylev , Matti Lassas