Related papers: Solution of the inverse spectral problem for a con…

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 consider the Robin problem for a uniformly elliptic divergence operator with measure data on the right-hand side of the equation and an absorption term on the boundary involving blowing up terms. We prove the existence of a positive…

For a second order formally symmetric elliptic differential expression we show that the knowledge of the Dirichlet-to-Neumann map or Robin-to-Dirichlet map for suitably many energies on an arbitrarily small open subset of the boundary…

This paper addresses inverse spectral problems associated with Dirac-type operators with a constant delay, specifically when this delay is less than one-third of the interval length. Our research focuses on eigenvalue behavior and operator…

In this study, singular diffusion operator with jump conditions is considered. Integral representations have been derived for solutions that satisfy boundary conditions and jump conditions. Some properties of eigenvalues and eigenfunctions…

In this paper the complete spectral analysis of the operators is carried out and also with help of generalized normalizing numbers the inverse problem is solved.

In this work, the Dirac-type integro di{\S}erential system with one classical boundary condition and another nonlocal integral boundary condition is considered. We obtain the asymptotic formulae for the solutions, eigenvalues and nodal…

Inverse problems of recovering the coefficients of Sturm-Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: (1) from the sequences of eigenvalues and norming constants; (2)…

The spectral behavior of the difference between the resolvents of two realizations $\tilde A_1$ and $\tilde A_2$ of a second-order strongly elliptic symmetric differential operator $A$, defined by different Robin conditions $\nu…

We consider inverse problems for wave, heat and Schr\"odinger-type operators and corresponding spectral problems on domains of ${\bf R}^n$ and compact manifolds. Also, we study inverse problems where coefficients of partial differential…

We present a technique for reconstructing a semi-infinite Jacobi operator in the limit circle case from the spectra of two different self-adjoint extensions. Moreover, we give necessary and sufficient conditions for two real sequences to be…

Let $\Omega =\omega\times\mathbb R$ where $\omega\subset \mathbb R^2$ be a bounded domain, and $V : \Omega \to\mathbb R$ a bounded potential which is $2\pi$-periodic in the variable $x_{3}\in \mathbb R$. We study the inverse problem…

We introduce a computer-assisted proof for the required number of electrodes for uniqueness and global reconstruction for the inverse Robin transmission problem, where the corrosion function on the boundary of an interior object is to be…

The inverse spectral problems are studied for the Sturm-Liouville operator on the star-shaped graph and for the matrix Sturm-Liouville operator with the boundary condition in the general self-adjoint form. We obtain necessary and sufficient…

With a densely defined symmetric semi-bounded operator of nonzero defect indexes $L_0$ in a separable Hilbert space ${\cal H}$ we associate a topological space $\Omega_{L_0}$ ({\it wave spectrum}) constructed from the reachable sets of a…

The inverse problem for the Sturm- Liouville operator with complex periodic potential and positive discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the…

We consider an inverse spectral problem with the third-order differential equation and the non-separated boundary conditions. Two theorems on the uniqueness of the solution of this problem are proved, and a method for establishing the…

In the paper, we study the problem of recovering the potential from the spectrum of the Dirichlet boundary value problem for a Sturm--Liouville equation with frozen argument on a closed set. We consider the case when the closed set consists…

For finite dimensional CMV matrices the classical inverse spectral problems are considered. We solve the inverse problem of reconstructing a CMV matrix by its Weyl's function, the problem of reconstructing the matrix by two spectra of CMV…

In the paper, Sturm--Liouville differential operators on time scales consisting of a finite number of isolated points and segments are considered. Such operators unify differential and difference operators. We obtain properties of their…