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Finite range perturbations of finite gap Jacobi and CMV operators
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2016 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 301, 204-226 p.Article in journal (Refereed) Published
Abstract [en]

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.
Keyword [en]
Jacobi operators, CMV operators, Spectral theorem, Orthogonal polynomials, Resonances
National Category
URN: urn:nbn:se:uu:diva-304134DOI: 10.1016/j.aim.2016.05.024ISI: 000382424900005OAI: oai:DiVA.org:uu-304134DiVA: diva2:1021265
Knut and Alice Wallenberg Foundation, KAW 2010.0063
Available from: 2016-10-04 Created: 2016-10-03 Last updated: 2016-10-04Bibliographically approved

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Kozhan, Rostyslav
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