Inverse problems for Jacobi operators with mixed spectral data
نویسندگان
چکیده
We consider semi-infinite Jacobi matrices with discrete spectrum. prove that a operator can be uniquely recovered from one spectrum and subsets of another norming constants c...
منابع مشابه
Inverse spectral problems for Sturm-Liouville operators with transmission conditions
Abstract: This paper deals with the boundary value problem involving the differential equation -y''+q(x)y=lambda y subject to the standard boundary conditions along with the following discontinuity conditions at a point y(a+0)=a1y(a-0), y'(a+0)=a2y'(a-0)+a3y(a-0). We develop the Hochestadt-Lieberman’s result for Sturm-Lio...
متن کاملInverse spectral analysis for finite matrix-valued Jacobi operators
Consider the Jacobi operators J given by (J y)n = anyn+1+bnyn+a∗n−1yn−1, yn ∈ C (here y0 = yp+1 = 0), where bn = b ∗ n and an : det an 6= 0 are the sequences of m × m matrices, n = 1, .., p. We study two cases: (i) an = a∗n > 0; (ii) an is a lower triangular matrix with real positive entries on the diagonal (the matrix J is (2m+1)-band mp×mp matrix with positive entries on the first and the las...
متن کاملTrace Formulas and Inverse Spectral Theory for Jacobi Operators
Based on high energy expansions and Herglotz properties of Green and Weyl m-functions we develop a self-contained theory of trace formulas for Jacobi operators. In addition, we consider connections with inverse spectral theory, in particular uniqueness results. As an application we work out a new approach to the inverse spectral problem of a class of reflectionless operators producing explicit ...
متن کاملSolving Inverse Problems with Spectral Data
We consider a two dimensional membrane. The goal is to find properties of the membrane or properties of a force on the membrane. The data is natural frequencies or mode shape measurements. As a result, the functional relationship between the data and the solution of our inverse problem is both indirect and nonlinear. In this paper we describe three distinct approaches to this problem. In the fi...
متن کاملSpectral Deformations of Jacobi Operators
We extend recent work concerning isospectral deformations for one-dimensional Schrödinger operators to the case of Jacobi operators. We provide a complete spectral characterization of a new method that constructs isospectral deformations of a given Jacobi operator (Hu)(n) = a(n)u(n + 1) + a(n − 1)u(n − 1) − b(n)u(n). Our technique is connected to Dirichlet data, that is, the spectrum of the ope...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Difference Equations and Applications
سال: 2021
ISSN: ['1026-7042', '1563-5120', '1023-6198']
DOI: https://doi.org/10.1080/10236198.2020.1867546