English
Related papers

Related papers: Inverse spectral Love problem via Weyl-Titchmarsh …

200 papers

In this paper we solve an inverse resonance problem for the half-solid with vanishing stresses on the surface: Lamb's problem. Using a semi-classical approach we are able to simplify this three-dimensional problem of the elastic wave…

Spectral Theory · Mathematics 2024-10-14 Samuele Sottile

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

In the paper we propose a direct method for recovering the Sturm-Liouville potential from the Weyl-Titchmarsh $m$-function given on a countable set of points. We show that using the Fourier-Legendre series expansion of the transmutation…

Classical Analysis and ODEs · Mathematics 2021-07-07 Vladislav V. Kravchenko , Sergii M. Torba

In this paper, we for the first time get constructive solution for the inverse Sturm-Liouville problem with complex-valued singular potential and with polynomials of the spectral parameter in the boundary conditions. The uniqueness of…

Spectral Theory · Mathematics 2023-09-11 Egor E. Chitorkin , Natalia P. Bondarenko

We analyze the inverse spectral problem on the half line associated with elastic surface waves. Here, we focus on Love waves. Under certain generic conditions, we establish uniqueness and present a reconstruction scheme for the S- wavespeed…

Analysis of PDEs · Mathematics 2019-08-29 Maarten V. de Hoop , Alexei Iantchenko , Robert D. van der Hilst , Jian Zhai

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

In this paper we study Love waves in a layered, elastic half-space. We first address the direct problem and we characterize the existence of Love waves through the dispersion relation. We then address the inverse problem and we show how to…

Analysis of PDEs · Mathematics 2024-04-09 Maarten V. de Hoop , Josselin Garnier , Alexei Iantchenko , Julien Ricaud

We analyze the inverse spectral problem on the half line associated with elastic surface waves. Here, we extend the treatment of Love waves [arXiv: 1908.10529] to Rayleigh waves. Under certain conditions, and assuming that the Poisson ratio…

Analysis of PDEs · Mathematics 2019-09-02 Maarten V. de Hoop , Alexei Iantchenko , Robert D. van der Hilst , Jian Zhai

The matrix Sturm-Liouville operator with an integrable potential on the half-line is considered. We study the inverse spectral problem, which consists in recovering of this operator by the Weyl matrix. The main result of the paper is the…

Spectral Theory · Mathematics 2014-12-19 Natalia Bondarenko

We study the question to what extent spectral information of a Schr\"odinger operator on a finite, compact metric graph subject to standard or $\delta$-type matching conditions can be recovered from a corresponding Titchmarsh-Weyl function…

Spectral Theory · Mathematics 2016-01-27 Jonathan Rohleder

We present a simple exact analytical solution, using the Weyl-Titchmarsh-Kodaira spectral theorem, for the spectral function of the one-dimensional diatomic molecule model consisting of two attractive delta function wells in the presence of…

Atomic Physics · Physics 2007-05-23 Gerald V. Dunne , Christopher S. Gauthier

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 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

We formulate an inverse problem for an uncoupled space-time fractional Schr\"odinger equation on closed manifolds. Our main goal is to determine the fractional powers and the Riemannian metric (up to an isometry) simultaneously from the…

Analysis of PDEs · Mathematics 2024-10-29 Li Li

A Borg-Marchenko type uniqueness theorem (in terms of the Weyl function) is obtained here for the system auxiliary to the N-wave equation. A procedure to solve inverse problem is used for this purpose. The asymptotic condition on the Weyl…

Mathematical Physics · Physics 2008-03-18 Alexander Sakhnovich

In this paper, a Sturm-Liouville boundary value problem equiped with conformable fractional derivates is considered. We give some uniqueness theorems for the solutions of inverse problems according to the Weyl function, two given spectra…

Classical Analysis and ODEs · Mathematics 2022-03-23 A. Sinan Ozkan , İbrahim Adalar

The inverse spectral problem is studied for the Sturm-Liouville operator with a complex-valued potential and arbitrary entire functions in one of the boundary conditions. We obtain necessary and sufficient conditions for uniqueness, and…

Spectral Theory · Mathematics 2021-09-01 Natalia Bondarenko

Inverse problem to recover the skew-self-adjoint Dirac-type system from the generalized Weyl matrix function is treated in the paper. Sufficient conditions under which the unique solution of the inverse problem exists, are formulated in…

Classical Analysis and ODEs · Mathematics 2010-02-02 B. Fritzsche , B. Kirstein , A. L. Sakhnovich

We analyze an inverse problem associated with the time-harmonic Rayleigh system on a flat elastic half-space concerning the recovery of Lam\'{e} parameters in a slab beneath a traction-free surface. We employ the Markushevich substitution,…

Analysis of PDEs · Mathematics 2024-01-15 Maarten V. de Hoop , Alexei Iantchenko

We study the inverse problem of recovering Sturm-Liouville operators on the half-line with a Bessel-type singularity inside the interval from the given Weyl function. The corresponding uniqueness theorem is proved, a constructive procedure…

Spectral Theory · Mathematics 2012-11-13 Alexey Fedoseev
‹ Prev 1 2 3 10 Next ›