Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic Jacobi operators

Abstract

We are interested in diagonal perturbations of a periodic Jacobi operator that introduce embedded eigenvalues in its essential spectrum. Embedding multiple points in the essential spectrum has been known to be difficult, given that eigenvalues are destroyed easily by small perturbations. However, given a finite or countably infinite set of points within an absolutely continuous band of the original periodic operator (subject only to a very weak non-resonance condition) we are able to construct a diagonal perturbation that preserves the essential spectrum and places eigenvalues in all of those points.

arXiv commentIt is combined with arXiv:1805.01569

References in corpus (5)

• Criteria for embedded eigenvalues for discrete Schrödinger operators
• Criteria for eigenvalues embedded into the absolutely continuous spectrum of perturbed Stark type operators
• Absence of singular continuous spectrum for perturbed discrete Schrödinger operators
• Embedded eigenvalues for perturbed periodic Jacobi operators using a geometric approach
• The asymptotical behaviour of embedded eigenvalues for perturbed periodic operators

Cited by in corpus (4)

• Criteria for embedded eigenvalues for discrete Schrödinger operators
• Absence of singular continuous spectrum for perturbed discrete Schrödinger operators
• Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators
• The asymptotical behaviour of embedded eigenvalues for perturbed periodic operators