Opuscula Math. 30, no. 2 (2010), 193-202

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.

Full text (pdf)

  • 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.
Opuscula Mathematica - cover

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

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.