Opuscula Math. 30, no. 2 (2010), 193-202
http://dx.doi.org/10.7494/OpMath.2010.30.2.193
Opuscula Mathematica
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.
- Beata Strack
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland
- Received: 2009-07-09.
- Revised: 2010-01-09.
- Accepted: 2010-01-18.
