Finite range perturbations of finite gap Jacobi and CMV operators

Abstract

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 [25, 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.

this is the full-details version of the paper accepted for publication in Advances in Mathematics 30 pages

References in corpus (3)

• Spectral Theory as Influenced by Fritz Gesztesy
• Spectral and resonance problem for perturbations of periodic Jacobi operators
• Meromorphic continuations of finite gap Herglotz functions and periodic Jacobi matrices

Cited by in corpus (1)

• Spectra of infinite graphs with tails