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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

Inverse spectral problems for Sturm-Liouville operators with nonlocal boundary conditions are studied. As the main spectral characteristics we introduce the so-called Weyl-type function and two spectra, which are generalizations of the…

Spectral Theory · Mathematics 2014-10-09 Vjacheslav Yurko , Chuan-Fu Yang

This paper deals with the Sturm-Liouville problem that feature distribution potential, polynomial dependence on the spectral parameter in the first boundary condition, and analytical dependence, in the second one. We study an inverse…

Spectral Theory · Mathematics 2024-09-05 E. E. Chitorkin , N. P. Bondarenko

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

The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary…

Spectral Theory · Mathematics 2014-07-15 Natalia Bondarenko

This note deals with the direct and inverse spectral analysis for a class of infinite band symmetric matrices. This class corresponds to operators arising from difference quations with usual and inner boundary conditions. We give a…

Mathematical Physics · Physics 2015-12-02 Mikhail Kudryavtsev , Sergio Palafox , Luis O. Silva

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 operator of double differentiation on a finite interval with Robin boundary conditions perturbed by the composition of a Volterra convolution operator and the differentiation one is considered. We study the inverse problem of recovering…

Spectral Theory · Mathematics 2020-01-28 S. A. Buterin , A. E. Choque Rivero

In the present paper, we consider a non self adjoint hyperbolic operator with a vector field and an electric potential that depend not only on the space variable but also on the time variable. More precisely, we attempt to stably and…

Analysis of PDEs · Mathematics 2018-10-05 Mourad Bellassoued , Ibtissem Ben Aïcha

Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…

Analysis of PDEs · Mathematics 2024-12-23 S. G. Pyatkov , O. A. Soldatov

We study the inverse problem of determining the coefficients of the fractional power of a general second order elliptic operator given in the exterior of an open subset of the Euclidean space. We show the problem can be reduced into…

Analysis of PDEs · Mathematics 2021-10-19 Tuhin Ghosh , Gunther Uhlmann

We study the inverse boundary value problem for the wave equation using the single-layer potential operator as the data. We assume that the data have frequency content in a bounded interval. We prove how to choose classes of nonsmooth…

Analysis of PDEs · Mathematics 2017-05-12 Kiril Datchev , Maarten V. de Hoop

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

Starting from the semi-classical spectrum of Schr\"odinger operators $-h^2\Delta+V$ (on $\mathbb{R}^n$ or on a Riemannian manifold) it is possible to detect critical levels of the potential $V$. Via micro-local methods one can express…

Analysis of PDEs · Mathematics 2013-02-25 Brice Camus

We consider the determination of an unknown potential $q(x)$ form a fractional diffusion equation subject to overposed lateral boundary data. We show that this data allows recovery of two spectral sequences for the associated inverse…

Mathematical Physics · Physics 2018-11-15 William Rundell , Masahiro Yamamoto

In this paper we consider a non-local problem for a Laplace operator in a multidimensional bounded symmetric domain. The investigated problem is an analogue of the classical periodic boundary value problems in the case of non-rectangular…

Analysis of PDEs · Mathematics 2016-08-22 Makhmud A. Sadybekov , Berikbol T. Torebek

We formulate the inverse spectral theory for a non-self-adjoint one-dimensional Dirac operator associated periodic potentials via a Riemann-Hilbert problem approach. We use the resulting formalism to solve the initial value problem for the…

Exactly Solvable and Integrable Systems · Physics 2025-05-09 Gino Biondini , Gregor Kovačič , Alexander Tovbis , Zachery Wolski , Zechuan Zhang

This paper is concerned with the inverse spectral problem for the third-order differential equation with distribution coefficient. The inverse problem consists in the recovery of the differential expression coefficients from the spectral…

Spectral Theory · Mathematics 2023-03-24 Natalia P. Bondarenko

In this paper, we consider a problem for the first order Dirac differential equations system with spectral parameter dependent in boundary condition. The asymptotic behaviors of eigenvalues, eigenfunctions and normalizing numbers of this…

Spectral Theory · Mathematics 2014-04-02 Kh. R. Mamedov , O. Akcay

We consider an inverse spectral problem that consists in the recovery of the differential expression coefficients for higher-order operators with separated boundary conditions from the spectral data (eigenvalues and weight numbers). This…

Spectral Theory · Mathematics 2023-11-10 Natalia P. Bondarenko