Opuscula Math. 30, no. 2 (2010), 193-202
A note on the discrete Schrödinger operator with a perturbed periodic potential
Abstract. The aim of this paper is to study the spectrum of the one-dimensional discrete Schrödinger operator with a perturbed periodic potential. We obtain natural conditions under which this perturbation preserves the essential spectrum of the considered operator. Conditions on the number of isolated eigenvalues are given.
Keywords: one-dimensional Schrödinger operator, Jacobi operator, perturbation of periodic potential, essential spectrum, discrete part of the spectrum.
Mathematics Subject Classification: 47B39, 47B37.
- Received: 2009-07-09.
- Revised: 2010-01-09.
- Accepted: 2010-01-18.