Related papers: A practical method for recovering Sturm-Liouville …
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…
Boundary value problems on hedgehog-type graphs for Sturm-Liouville differential operators with general matching conditions are studied. We investigate inverse spectral problems of recovering the coefficients of the differential equation…
An interesting inverse optimization spectral problem, with important applications in structural health monitoring and damage detection, material design, seismic wave analysis, sonar detection, and related fields, involves reconstructing a…
This paper is devoted to the study of a partial inverse spectral problem for Sturm-Liouville operators with frozen arguments on a star-shaped graph. The potentials are assumed to be known a priori on all edges except one, and the objective…
In this paper we study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from two spectra. We give a reconstruction algorithm and establish existence and uniqueness of reconstruction. Our approach…
An inverse scattering method based on an auxiliary inverse Sturm-Liouville problem recently proposed by Horv\'ath and Apagyi [Mod. Phys. Lett. B 22, 2137 (2008)] is examined in various aspects and developed further to (re)construct…
In this paper, we explore the inverse spectral problem of Sturm-Liouville operator on a star-like graph. To this fixed star-like graph centered at the origin as its vertex, we attach $m$ edges. On each edge, we impose the Sturm-Liouville…
The representations of the kernels of the transmutation operator and of its inverse relating the one-dimensional Schr\"odinger operator with the second derivative are obtained in terms of the eigenfunctions of a corresponding…
We give a complete description of the set of spectral data (eigenvalues and specially introduced norming constants) for Sturm--Liouville operators on the interval $[0,1]$ with matrix-valued potentials in the Sobolev space $W_2^{-1}$ and…
In this paper we prove an inverse resonance theorem for the half-solid with vanishing stresses on the surface via Weyl-Titchmarsh function. Using a semi-classical approach it is possible to simplify this three-dimensional problem of the…
On the space $L^{2}(\mathbb{R})$ the Sturm-Liouville operator $L$ with certain behavior of the potential at infinity is considered. It is proved that $L$ is uniquely determined by its scattering data. The recovery of $L$ is reduced to the…
We consider the non-self-adjoint Sturm-Liouville operator on a finite interval. The inverse spectral problem is studied, which consists in recovering this operator from its eigenvalues and generalized weight numbers. We prove local…
In arXiv:1306.2914 a method for approximate solution of Sturm-Liouville equations and related spectral problems was presented based on the construction of the Delsarte transmutation operators. The problem of numerical approximation of…
This paper deals with the inverse spectral problem for a non-self-adjoint Sturm-Liouville operator with discontinuous conditions inside the interval. We obtain that if the potential $q$ is known a priori on a subinterval $ \left[ b,\pi…
The paper deals with two inverse problems for Sturm--Liouville operator $Ly=-y" +q(x)y$ on the finite interval $[0,\pi]$. The first one is the problem of recovering of a potential by two spectra. We associate with this problem the map $F:\,…
The Sturm-Liouville operator with singular potentials on the lasso graph is considered. We suppose that the potential is known a priori on the boundary edge, and recover the potential on the loop from a part of the spectrum and some…
The perturbation of the Sturm-Liouville operator on a finite interval with Dirichlet boundary conditions by a convolution operator is considered. Local stability and global unique solvability of the inverse problem of recovering the…
We propose a discrete approach for solving an inverse problem for Schr\"odinger's equation in two dimensions, where the unknown potential is to be determined from boundary measurements of the Dirichlet to Neumann map. For absorptive…
A method for solving spectral problems for the Sturm-Liouville equation $(pv^{\prime})^{\prime}-qv+\lambda rv=0$ based on the approximation of the Delsarte transmutation operators combined with the Liouville transformation is presented. The…
We study Sturm--Liouville differential operators on the time scales consisting of a finite number of isolated points and segments. In a previous paper it was established that such operators are uniquely determined by their spectral…