Spectral and resonance problem for perturbations of periodic Jacobi operators
Classical Analysis and ODEs
2014-09-23 v3 Mathematical Physics
math.MP
Spectral Theory
Abstract
Necessary and sufficient conditions are presented for a measure to be the spectral measure of a finite range or exponentially decaying perturbation of a periodic Jacobi operator. As a corollary we can fully solve the inverse resonance problem: given resonances and eigenvalues we can recover the spectral measure of the Jacobi operator; we provide necessary and sufficient conditions under which such an operator exists and is unique; and we show that the inverse resonance problem is stable under small perturbations.
Keywords
Cite
@article{arxiv.1211.4274,
title = {Spectral and resonance problem for perturbations of periodic Jacobi operators},
author = {Rostyslav Kozhan},
journal= {arXiv preprint arXiv:1211.4274},
year = {2014}
}
Comments
42pp