Embedded eigenvalues for perturbed periodic Jacobi operators using a geometric approach

Abstract

We consider the problem of embedding eigenvalues into the essential spectrum of periodic Jacobi operators, using an oscillating, decreasing potential. To do this we employ a geometric method, previously used to embed eigenvalues into the essential spectrum of the discrete Schrödinger operator. For periodic Jacobi operators we relax the rational dependence conditions on the values of the quasi-momenta from this previous work. We then explore conditions that permit not just the existence of infinitely many subordinate solutions to the formal spectral equation but also the embedding of infinitely many eigenvalues.

arXiv commentAccepted for publication in Journal of Difference Equations and Applications, March 2018

References in corpus (2)

• On the discrete spectrum of complex banded matrices
• Eigenvalues for perturbed periodic Jacobi matrices by the Wigner-von Neumann approach

Cited by in corpus (4)

• Topics on Fermi varieties of discrete periodic Schrödinger operators
• Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators
• Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic Jacobi operators
• Sharp bounds for finitely many embedded eigenvalues of perturbed Stark type operators