Spectrum of the one-dimensional Schrödinger operator with a periodic potential subjected to a local dilative perturbation

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Abstract

We study the spectrum of the one-dimensional Schrödinger operator with a potential, whose periodicity is violated via a local dilation. We obtain conditions under which this violation preserves the essential spectrum of the Schrödinger operator and an infinite number of isolated eigenvalues appear in a gap of the essential spectrum. We show that the considered perturbation of the periodic potential is not relative compact in general.

Original languageEnglish
Pages (from-to)573-589
Number of pages17
JournalIntegral Equations and Operator Theory
Volume58
Issue number4
DOIs
StatePublished - Aug 2007

Bibliographical note

Funding Information:
Supported by KAMEA Project for scientific Absorption in Israel and partially by the German-Israeli Foundation (GIF), grant number I-619-17.6/2001.

Keywords

  • Discrete part of the spectrum
  • Essential spectrum
  • Perturbation of a periodic potential
  • Schrödinger operator

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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