English

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