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On the essential spectrum of a class of singular matrix differential operators. II. Weyl's limit circles for the Hain-Lust operator whenever quasi-regularity conditions are not satisfied

Kurasov, Pavel LU ; Lelyavin, Igor and Naboko, Serguei (2008) In Proceedings of the Royal Society of Edinburgh. Section A 138(1). p.109-138
Abstract
The essential spectrum of the singular matrix differential operator of mixed order determined by the operator matrix [GRAPHICS] is studied. Investigation of the essential spectrum of the corresponding self-adjoint operator is continued but; now without assuming that the quasi-regularity conditions are satisfied. New conditions that guarantee that the operator is semi-bounded from below are derived. It is proven that the essential spectrum of any self-adjoint operator associated with the matrix differential operator is given by the range range((mp - beta(2))/px(2)) in the case where the quasi-regularity conditions are not satisfied.
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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Proceedings of the Royal Society of Edinburgh. Section A
volume
138
issue
1
pages
109 - 138
publisher
Cambridge University Press
external identifiers
  • wos:000253780800005
  • scopus:48749121961
ISSN
0308-2105
DOI
10.1017/S0308210506000576
language
English
LU publication?
yes
id
e431abb5-4b9c-4bea-8c08-3d64ecd85ba4 (old id 1191714)
date added to LUP
2016-04-01 14:56:29
date last changed
2025-01-04 07:09:00
@article{e431abb5-4b9c-4bea-8c08-3d64ecd85ba4,
  abstract     = {{The essential spectrum of the singular matrix differential operator of mixed order determined by the operator matrix [GRAPHICS] is studied. Investigation of the essential spectrum of the corresponding self-adjoint operator is continued but; now without assuming that the quasi-regularity conditions are satisfied. New conditions that guarantee that the operator is semi-bounded from below are derived. It is proven that the essential spectrum of any self-adjoint operator associated with the matrix differential operator is given by the range range((mp - beta(2))/px(2)) in the case where the quasi-regularity conditions are not satisfied.}},
  author       = {{Kurasov, Pavel and Lelyavin, Igor and Naboko, Serguei}},
  issn         = {{0308-2105}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{109--138}},
  publisher    = {{Cambridge University Press}},
  series       = {{Proceedings of the Royal Society of Edinburgh. Section A}},
  title        = {{On the essential spectrum of a class of singular matrix differential operators. II. Weyl's limit circles for the Hain-Lust operator whenever quasi-regularity conditions are not satisfied}},
  url          = {{http://dx.doi.org/10.1017/S0308210506000576}},
  doi          = {{10.1017/S0308210506000576}},
  volume       = {{138}},
  year         = {{2008}},
}