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Singular Indefinite Sturm‐Liouville Operators with a Spectral Gap
Author(s) -
Behrndt Jussi,
Möws Roland,
Trunk Carsten
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910304
Subject(s) - sturm–liouville theory , eigenvalues and eigenvectors , mathematics , limit (mathematics) , spectrum (functional analysis) , mathematical analysis , singular solution , pure mathematics , singular integral operators , mathematical physics , spectral analysis , operator theory , physics , fourier integral operator , quantum mechanics , spectroscopy , boundary value problem
Singular Sturm‐Liouville operators with the indefinite weight sgn(·) and a symmetric potential which has a positive limit at ∞ have a gap in the essential spectrum. Under an additional condition it is shown that in this gap are no eigenvalues. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)