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

Beata Strack

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.

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  • 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.
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Cite this article as:
Beata Strack, A note on the discrete Schrödinger operator with a perturbed periodic potential, Opuscula Math. 30, no. 2 (2010), 193-202, http://dx.doi.org/10.7494/OpMath.2010.30.2.193

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