Inverse spectral problems for Jacobi matrix with finite perturbed parameters - Nizhnik, L. P. (Methods of Functional Analysis and Topology, 2015)
For Jacobi matrices with finitely perturbed parameters, we get an explicit representation of the Weyl function, and solve inverse spectral problems, that is, we recover Jacobi matrices from spectral data. For the spectral data, we take the following: the spectral density of the absolutely continuous spectrum, with or without all the eigenvalues; the numerical parameters of the representation of one component of the vector-eigenfunction in terms of Chebyshev polynomials. We prove that these inverse problems have a unique solution, or only a finite number of solutions.