Related papers: Two inverse spectral problems for a class of singu…
In this paper we consider a class of isospectral deformations of the inhomogeneous string boundary value problem. The deformations considered are generalizations of the isospectral deformation that has arisen in connection with the…
This paper revisits the classical problem "Can we hear the density of a string?", which can be formulated as an inverse spectral problem for a Sturm-Liouville operator. Based on inverting a sequence of trace formulas, we propose a new…
A reference potential approach to the one-dimensional quantum-mechanical inverse problem is developed. All spectral characteristics of the system, including its discrete energy spectrum, the full energy dependence of the phase shift, and…
In this paper, we consider Barcilon's inverse problem, which consists of the recovery of the fourth-order differential operator from three spectra. We obtain the relationship of Barcilon's three spectra with the Weyl-Yurko matrix. Moreover,…
We consider canonical systems (with $2p\times 2p$ Hamiltonians $H(x)\geq 0$), which correspond to matrix string equations. Direct and inverse problems are solved in terms of Titchmarsh--Weyl and spectral matrix functions and related…
An inverse problem in spectroscopy is considered. The objective is to restore the discrete spectrum from observed spectrum data, taking into account the spectrometer's line spread function. The problem is reduced to solution of a system of…
This is part of a series of papers on the inverse spectral problem for bounded analytic plane domains. Here, we use the trace formula established in the first paper (`Balian-Bloch trace formula') to explicitly calculate wave trace…
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…
We consider a two-spectra inverse problem for the one-dimensional Schr\"{o}dinger equation with boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter and provide a complete solution of this…
A recently proposed discrete version of the Schrodinger spectral problem is considered. The whole hierarchy of differential-difference nonlinear evolution equations associated to this spectral problem is derived. It is shown that a discrete…
In this article the authors continue the discussion in \cite{ALM} about inverse problems for second order elliptic and hyperbolic equations on metric trees from boundary measurements. In the present paper we prove the identifiability of…
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…
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…
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…
We analyze in detail three classes of isomondromy deformation problems associated with integrable systems. The first two are related to the scaling invariance of the $n\times n$ AKNS hierarchies and the Gel'fand-Dikii hierarchies. The third…
In the paper, we study an inverse spectral problem for quadratic pencils of the Sturm--Liouville operators with singular coefficients and entire functions in the boundary conditions. We prove that a subspectrum is sufficient for recovering…
A new method for solving inverse spectral problems on quantum star graphs is proposed. The method is based on Neumann series of Bessel functions representations for solutions of Sturm-Liouville equations. The representations admit estimates…
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…
An inverse spectral problem for the Sturm-Liouville operator with a singular potential from the class $W_2^{-1}$ is solved by the method of spectral mappings. We prove the uniqueness theorem, develop a constructive algorithm for solution,…
We consider an inverse spectral problem for infinite linear mass-spring systems with different configurations obtained by changing the first mass. We give results on the reconstruction of the system from the spectra of two configurations.…