Finite range perturbations of finite gap Jacobi and CMV operators
2016 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 301, 204-226 p.Article in journal (Refereed) Published
Necessary and sufficient conditions are presented for a measure to be the spectral measure of a finite range perturbation of a Jacobi or CMV operator from a finite gap isospectral torus. The special case of eventually periodic operators solves an open problem of Simon [28, D.2.7]. We also solve the inverse resonance problem: it is shown that an operator is completely determined by the set of its eigen-values and resonances, and we provide necessary and sufficient conditions on their configuration for such an operator to exist.
Place, publisher, year, edition, pages
2016. Vol. 301, 204-226 p.
Jacobi operators, CMV operators, Spectral theorem, Orthogonal polynomials, Resonances
IdentifiersURN: urn:nbn:se:uu:diva-304134DOI: 10.1016/j.aim.2016.05.024ISI: 000382424900005OAI: oai:DiVA.org:uu-304134DiVA: diva2:1021265
FunderKnut and Alice Wallenberg Foundation, KAW 2010.0063