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An estimate on the non‐real spectrum of a singular indefinite Sturm‐Liouville operator
Author(s) -
Behrndt Jussi,
Gsell Bernhard,
Schmitz Philipp,
Trunk Carsten
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710397
Subject(s) - sturm–liouville theory , spectrum (functional analysis) , operator (biology) , radius , mathematics , mathematical analysis , pure mathematics , mathematical physics , physics , chemistry , quantum mechanics , computer science , boundary value problem , biochemistry , computer security , repressor , transcription factor , gene
It will be shown with the help of the Birman‐Schwinger principle that the non‐real spectrum of the singular indefinite Sturm‐Liouville operator sgn(·)(−d 2 /d x 2 + q ) with a real potential q ∈ L 1 ∩ L 2 is contained in a circle around the origin with radius ‖ q ‖ L 1 2 . (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)