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On the essential spectrum of a class of singular matrix differential operators. I: Quasiregularity conditions and essential self-adjointness

Kurasov, Pavel LU and Naboko, S (2002) In Mathematical Physics, Analysis and Geometry 5(3). p.243-286
Abstract
The essential spectrum of singular matrix differential operator determined by the operator matrix (-d/dx rho(x)d/dx + q(x) d/dx . beta/x - beta/x . d/dx m(x)/x(2))) is studied. It is proven that the essential spectrum of any self-adjoint operator associated with this expression consists of two branches. One of these branches (called regularity spectrum) can be obtained by approximating the operator by regular operators (with coefficients which are bounded near the origin), the second branch (called singularity spectrum) appears due to singularity of the coefficients.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
essential spectrum, quasiregularity conditions, Hain-Lust operator
in
Mathematical Physics, Analysis and Geometry
volume
5
issue
3
pages
243 - 286
publisher
Kluwer
external identifiers
  • wos:000180434700002
  • scopus:3142731536
ISSN
1385-0172
DOI
10.1023/A:1020929007538
language
English
LU publication?
yes
id
89cb5172-ddba-4f03-84d9-d29b13ebd31f (old id 319748)
date added to LUP
2007-11-05 14:05:03
date last changed
2017-07-30 04:36:17
@article{89cb5172-ddba-4f03-84d9-d29b13ebd31f,
  abstract     = {The essential spectrum of singular matrix differential operator determined by the operator matrix (-d/dx rho(x)d/dx + q(x) d/dx . beta/x - beta/x . d/dx m(x)/x(2))) is studied. It is proven that the essential spectrum of any self-adjoint operator associated with this expression consists of two branches. One of these branches (called regularity spectrum) can be obtained by approximating the operator by regular operators (with coefficients which are bounded near the origin), the second branch (called singularity spectrum) appears due to singularity of the coefficients.},
  author       = {Kurasov, Pavel and Naboko, S},
  issn         = {1385-0172},
  keyword      = {essential spectrum,quasiregularity conditions,Hain-Lust operator},
  language     = {eng},
  number       = {3},
  pages        = {243--286},
  publisher    = {Kluwer},
  series       = {Mathematical Physics, Analysis and Geometry},
  title        = {On the essential spectrum of a class of singular matrix differential operators. I: Quasiregularity conditions and essential self-adjointness},
  url          = {http://dx.doi.org/10.1023/A:1020929007538},
  volume       = {5},
  year         = {2002},
}