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Essential spectrum of Schrödinger operators with δ‐interactions on the union of compact Lipschitz hypersurfaces
Author(s) -
Behrndt Jussi,
Exner Pavel,
Lotoreichik Vladimir
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310254
Subject(s) - lipschitz continuity , operator (biology) , spectrum (functional analysis) , mathematics , essential spectrum , pure mathematics , schrödinger's cat , lipschitz domain , mathematical analysis , physics , chemistry , quantum mechanics , biochemistry , repressor , transcription factor , gene
In this note we prove that the essential spectrum of a Schrödinger operator with δ‐potential supported on a finite number of compact Lipschitz hypersurfaces is given by [0, +∞). We emphasize that the union of a family of Lipschitz hypersurfaces is in general not Lipschitz. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)