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A Remark on The Essential Spectra of Dirac Systems
Author(s) -
Schmidt Karl Michael
Publication year - 2000
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609399006463
Subject(s) - mathematics , spectrum (functional analysis) , dirac operator , essential spectrum , cover (algebra) , operator (biology) , dirac (video compression format) , real line , line (geometry) , spectral line , pure mathematics , algebra over a field , mathematical analysis , mathematical physics , quantum mechanics , physics , geometry , chemistry , neutrino , mechanical engineering , biochemistry , repressor , transcription factor , engineering , gene
A potential for the one‐dimensional Dirac operator is constructed such that its essential spectrum does not cover the whole real line, whereas the potential q ( x ) tends to ∞ as ∣ x ∣ → ∞. Furthermore, a criterion by Hartman and Wintner for points of the essential spectrum of Sturm–Liouville operators is generalised to a purely operator‐theoretical setting, and a simplified proof is given. 1991 Mathematics Subject Classification 34L40, 47A10, 81Q10.
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