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Name:
Miloslav Znojil
Reviewer number:
9689
Email:
znojil@ujf.cas.cz
Item's zbl-Number:
DE 018 614 994
Author(s):
Ikuta, Tadashi; Shima, Kazuhisa:
Shorttitle:
Spectrum of Dirac operators by the local compactness method
Source:
Proc. Am. Math. Soc. 131, No. 5, 1471-1479 (2003)
Classification:
81Q10Selfadjoint operator theory in quantum theory, including spectral analysis
Primary Classification:
34L05General spectral theory
Secondary Classification:
34L40Particular operators Dirac, one-dimensional Schroedinger, etc.
Keywords:
locally compact operator; Dirac operator; essential spectrum; discrete spectrum
Review:

The possible structures of spectra of the Dirac operators are
investigated under suitable assumptions about the (mainly,
asymptotics of the) four-by-four matrix potential V. On the basis of
the proof of the locally compact character of the operator (inspired
by the Enss' geometric approach and summarized here in three
theorems), the authors derive and prove a sufficient condition for
the existence of a purely discrete part of the spectrum, and confirm
the existence of the current ``positive- and negative-energy sea" of
the essential spectrum studied in terms of the so called Zhislin's
sequences.
Remarks to the editors:

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