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

Leonid Zelenko

doi:10.1007/s00020-007-1515-z

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

Leonid Zelenko

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	573-589
Number of pages	17
Journal	Integral Equations and Operator Theory
Volume	58
Issue number	4
DOIs	https://doi.org/10.1007/s00020-007-1515-z
State	Published - 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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10.1007/s00020-007-1515-z

Cite this

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abstract = "We study the spectrum of the one-dimensional Schr{\"o}dinger 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 Schr{\"o}dinger 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.",

keywords = "Discrete part of the spectrum, Essential spectrum, Perturbation of a periodic potential, Schr{\"o}dinger operator",

author = "Leonid Zelenko",

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N2 - 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.

AB - 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.

KW - Discrete part of the spectrum

KW - Essential spectrum

KW - Perturbation of a periodic potential

KW - Schrödinger operator

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ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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