Related papers: Inverse Problems for Jacobi Operators with Mixed S…
We give a short review of results on inverse spectral problems for ordinary differential operators on a spatial networks (geometrical graphs). We pay the main attention to the most important nonlinear inverse problems of recovering…
In this paper, we consider a class of matrix functions, which contains regularization matrices of Mirzoev and Shkalikov for differential operators with distribution coefficients of order $n \ge 2$. We show that every matrix function of this…
We consider inverse boundary value problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity…
We consider the problem of embedding eigenvalues into the essential spectrum of periodic Jacobi operators, using an oscillating, decreasing potential. To do this we employ a geometric method, previously used to embed eigenvalues into the…
Inverse spectral problem for a self-adjoint differential operator, which is the sum of the operator of the third derivative on a finite interval and of the operator of multiplication by a real function (potential), is solved. Closed system…
The Schroedinger equation on the half line is considered with a real-valued, integrable potential having a finite first moment. It is shown that the potential and the boundary conditions are uniquely determined by the data containing the…
Inverse spectral problems consist in recovering operators by their spectral characteristics. The problem of recovering the Sturm-Liouville operator with one frozen argument was studied earlier in works of various authors. In this paper, we…
We consider symmetric Jacobi operators with recurrence coefficients such that the corresponding difference equation is in the limit circle case. Equivalently, this means that the associated moment problem is indeterminate. Our main goal is…
The inverse problem for the Sturm- Liouville operator 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 is…
We look for spectral type differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with…
Spectral averaging techniques for one-dimensional discrete Schroedinger operators are revisited and extended. In particular, simultaneous averaging over several parameters is discussed. Special focus is put on proving lower bounds on the…
The paper concerns with infinite symmetric block Jacobi matrices $\bf J$ with $p\times p$-matrix entries. We present new conditions for general block Jacobi matrices to be selfadjoint and have discrete spectrum. In our previous papers there…
A third order self-adjoint differential operator with periodic boundary conditions and an one-dimensional perturbation has been considered. For this operator, we first show that the spectrum consists of simple eigenvalues and finitely many…
In this article, the inverse scattering problem (ISP) of recovering the matrix coefficient of a first order system of ordinary differential equations on the half-axis from its scattering matrix is considered. In the case of a triangular…
Solving inverse scattering problem for a discrete Sturm-Liouville operator with the fast decreasing potential one gets reflection coefficients $s_\pm$ and invertible operators $I+H_{s_\pm}$, where $ H_{s_\pm}$ is the Hankel operator related…
In this paper, we first develop a notion of dominated splitting for $\mathbb M(2,\mathbb C)$-sequences and show it is a stable property under $\|\cdot \|_\infty$-perturbation. Then we show an energy parameter belongs to the spectrum of a…
In this paper we study spectral properties of Jacobi operators. In particular, we prove two main results: (1) that perturbing the diagonal coefficients of Jacobi operator, in an appropriate sense, results in exponential localization, and…
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.
Spectral methods are an efficient way to solve partial differential equations on domains possessing certain symmetries. The utility of a method depends strongly on the choice of spectral basis. In this paper we describe a set of bases built…
When the coefficients of a Jacobi operator are finitely supported perturbations of the 1 and 0 sequences, respectively, the left reflection coefficient is a rational function whose poles inside, respectively outside, the unit disk…