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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
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
Royal Society of Edinburgh
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
2008-09-08 17:37:01
date last changed
2017-03-19 03:58:59
@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    = {Royal Society of Edinburgh},
  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},
  volume       = {138},
  year         = {2008},
}