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We consider an inverse problem for Laplacians on rotationally symmetric manifolds, which are finite for the transversal direction and periodic with respect to the axis of the manifold, i.e., Laplacians on tori. We construct an infinite…

Spectral Theory · Mathematics 2019-01-31 Hiroshi Isozaki , Evgeny L. Korotyaev

The inverse nodal problem for Dirac type integro-differential operator with the spectral parameter in the boundary conditions is studied. We prove that dense subset of the nodal points determines the coefficients of differential part of…

Spectral Theory · Mathematics 2017-11-27 Baki Keskin , H. Dilara Tel

We study the inverse problem of recovering a tree graph together with the weights on its edges (equivalently a metric tree) from the knowledge of the Dirichlet-to-Neumann matrix associated with the Laplacian. We prove an explicit formula…

Mathematical Physics · Physics 2021-04-05 Hannes Gernandt , Jonathan Rohleder

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

In this work, we consider Dirac-type operators with a constant delay less than half of the interval and not less than two-fifths of the interval. For our considered Dirac-type operators, two inverse spectral problems are studied.…

Spectral Theory · Mathematics 2023-05-31 Feng Wang , Chuan-Fu Yang

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

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

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

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

The inverse spectral problem is investigated for the matrix Sturm-Liouville equation on a finite interval. Properties of spectral characteristics are provided, a constructive procedure for the solution of the inverse problem along with…

Spectral Theory · Mathematics 2011-11-15 Natalia Bondarenko

We consider a pencil of matrix Sturm-Liouville operators on a finite interval. We study properties of its spectral characteristics and inverse problems that consist in recovering of the pencil by the spectral data: eigenvalues and…

Spectral Theory · Mathematics 2015-09-22 Natalia Bondarenko

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

A transfer matrix function representation of the fundamental solution of the general-type discrete Dirac system, corresponding to rectangular Schur coefficients and Weyl functions, is obtained. Connections with Szeg\"o recurrence, Schur…

Spectral Theory · Mathematics 2016-11-03 B. Fritzsche , B. Kirstein , I. Roitberg , A. L. Sakhnovich

The principal purpose of this note is to provide a reconstruction procedure for distributional matrix-valued potential coefficients of Schr\"odinger-type operators on a half-line from the underlying Weyl-Titchmarsh function.

Spectral Theory · Mathematics 2015-03-23 Jonathan Eckhardt , Fritz Gesztesy , Roger Nichols , Alexander Sakhnovich , Gerald Teschl

We consider the inverse problem for the dynamical system with discrete Schr\"odinger operator and discrete time. As an inverse data we take a \emph{response operator}, the natural analog of the dynamical Dirichlet-to-Neumann map. We derive…

Analysis of PDEs · Mathematics 2025-05-27 A. S. Mikhaylov , A. S. Mikhaylov

In this paper, inverse spectral problems for Sturm-Liouville operators on a tree (a graph without cycles) are studied. We show that if the potential on an edge is known a priori, then b - 1 spectral sets uniquely determine the potential…

Spectral Theory · Mathematics 2016-09-13 Natalia Bondarenko , Chung-Tsun Shieh

A non-classical Weyl theory is developed for Dirac systems with rectangular matrix potentials. The notion of the Weyl function is introduced and the corresponding direct problem is treated. Furthermore, explicit solutions of the direct and…

Spectral Theory · Mathematics 2012-11-29 B. Fritzsche , B. Kirstein , I. Ya. Roitberg , A. L. Sakhnovich

We study an inverse spectral problem for arbitrary order ordinary differential equations on compact star-type graphs when differential equations have regular singularities at boundary vertices. As the main spectral characteristics we…

Spectral Theory · Mathematics 2014-10-09 Vjacheslav Yurko

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 the inverse problem for countable, locally finite electrical networks with edge weights in an arbitrary field. The electrical inverse problem seeks to determine the weights of the edges knowing only the potential and current…

Combinatorics · Mathematics 2016-05-31 David Jekel