Finite range perturbations of finite gap Jacobi and CMV operators

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• 作者：Rostyslav Kozhan ^{kozhan@math.uu.se" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Jacobi operators ; CMV operators ; Spectral theorem ; Orthogonal polynomials ; Resonances
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：1 October 2016
• 年：2016
• 卷：301
• 期：Complete
• 页码：204-226
• 全文大小：492 K

文摘

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 eigenvalues and resonances, and we provide necessary and sufficient conditions on their configuration for such an operator to exist.