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arXiv · 1211.4274

Spectral and resonance problem for perturbations of periodic Jacobi operators

Rostyslav Kozhan
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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.

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Rostyslav Kozhan. 2014-09-19. Spectral and resonance problem for perturbations of periodic Jacobi operators. https://arxiv.org/abs/1211.4274

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