相关论文: Inverse spectral analysis for finite matrix-valued…
We consider the dynamic problems for the discrete systems with discrete time associated with finite and semi-infinite Jacobi matrices. The result of the paper is a procedure of association of special Hilbert spaces of functions, namely de…
Our main result asserts that a certain natural non-linear operator on Jacobi matrices built by a hyperbolic polynomial with real Julia set is a contraction in operator norm if the polynomial is sufficiently hyperbolic. This allows us to get…
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,…
In this article we consider the Markovian products of invertible (not necessarily positive) matrices chosen from a strongly irreducible, contracting, finite set of matrices. We construct Markovian transfer operators and prove the spectral…
We study the trace class perturbations of the whole-line, discrete Laplacian and obtain a new bound for the perturbation determinant of the corresponding non-self-adjoint Jacobi operator. Based on this bound, we refine the Lieb--Thirring…
We establish a correspondence between the semi-infinite and infinite Volterra lattices having a finite logarithmic Hamiltonian and certain classes of even probability measures. In doing so, we apply the inverse spectral theory of Jacobi…
The inverse eigenvalue problem of a given graph $G$ is to determine all possible spectra of real symmetric matrices whose off-diagonal entries are governed by the adjacencies in $G$. Barrett et al. introduced the Strong Spectral Property…
We prove new spectral enclosures for the non-real spectrum of a class of $2\times2$ block operator matrices with self-adjoint operators $A$ and $D$ on the diagonal and operators $B$ and $-B^*$ as off-diagonal entries. One of our main…
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…
In this work, we study inverse resonance problems for the Schr\"odinger operator on the real line with the potential supported in $[0,1]$. In general, all eigenvalues and resonances can not uniquely determine the potential. (i) It is shown…
We consider operator matrices {\bf H}= (A_0 B_{01} \\ B_{10} A_{1}) with self-adjoint entries A_i, i=0,1, and bounded B_{01}=B_{10}^*, acting in the orthogonal sum {\cal H}={\cal H}_0\oplus{\cal H}_1 of Hilbert spaces {\cal H}_0 and {\cal…
We consider an inverse spectral problem on a quantum graph associated with the square lattice. Assuming that the potentials on the edges are compactly supported and symmetric, we show that the Dirichlet-to-Neumann map for a boundary value…
We develop a spectral analysis of a class of block Jacobi operators based on the conjugate operator method of Mourre. We give several applications including scalar Jacobi operators with periodic coefficients, a class of difference operators…
In this paper we discuss the spectral properties of one-term symmetric differential operators of even order with interior singularity, namely, we determine the deficiency numbers, describe its self-adjoint extensions and their spectrum. It…
The study of solving the inverse eigenvalue problem for nonnegative matrices has been around for decades. It is clear that an inverse eigenvalue problem is trivial if the desirable matrix is not restricted to a certain structure. Provided…
A classical theorem of Wendroff shows that one may reconstructs a sequence of orthogonal polynomials on the real line from two non-constant polynomials of consecutive degrees whose zeros strictly interlace on the real line. In this note we…
We consider the Hamburger, Stieltjes and Hausdorff moment problems, that are problems of the construction of a Borel measure supported on a real line, on a half-line or on an interval $(0,1)$, from a prescribed set of moments. We propose a…
We present a comprehensive treatment of relative oscillation theory for finite Jacobi matrices. We show that the difference of the number of eigenvalues of two Jacobi matrices in an interval equals the number of weighted sign-changes of the…
The inverse of the metric matrices on the Siegel-Jacobi upper half space ${\mathcal{X}}^J_n$, invariant to the restricted real Jacobi group $G^J_n(\mathbb{R})_0$ and extended Siegel-Jacobi $\tilde{{\mathcal{X}}}^J_n$ upper half space,…
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…