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Persistence of embedded eigenvalues

Agmon, Shmuel; Herbst, Ira and Maad Sasane, Sara LU (2011) In Journal of Functional Analysis 261(2). p.451-477
Abstract
We consider conditions under which an embedded eigenvalue of a self-adjoint operator remains embedded under small perturbations. In the case of a simple eigenvalue embedded in continuous spectrum of multiplicity m<∞m<∞ we show that in favorable situations, the set of small perturbations of a suitable Banach space which do not remove the eigenvalue form a smooth submanifold of codimension m. We also have results regarding the cases when the eigenvalue is degenerate or when the multiplicity of the continuous spectrum is infinite.
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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
embedded eigenvalues, perturbation
in
Journal of Functional Analysis
volume
261
issue
2
pages
27 pages
publisher
Elsevier
external identifiers
  • scopus:79954974251
ISSN
0022-1236
DOI
10.1016/j.jfa.2010.09.005
language
English
LU publication?
no
id
0679744b-5655-4ff2-89c5-a76abee660ca
date added to LUP
2017-02-08 13:20:19
date last changed
2017-06-25 04:59:04
@article{0679744b-5655-4ff2-89c5-a76abee660ca,
  abstract     = {We consider conditions under which an embedded eigenvalue of a self-adjoint operator remains embedded under small perturbations. In the case of a simple eigenvalue embedded in continuous spectrum of multiplicity m&lt;∞m&lt;∞ we show that in favorable situations, the set of small perturbations of a suitable Banach space which do not remove the eigenvalue form a smooth submanifold of codimension m. We also have results regarding the cases when the eigenvalue is degenerate or when the multiplicity of the continuous spectrum is infinite.},
  author       = {Agmon, Shmuel and Herbst, Ira and Maad Sasane, Sara},
  issn         = {0022-1236},
  keyword      = {embedded eigenvalues,perturbation},
  language     = {eng},
  number       = {2},
  pages        = {451--477},
  publisher    = {Elsevier},
  series       = {Journal of Functional Analysis},
  title        = {Persistence of embedded eigenvalues},
  url          = {http://dx.doi.org/10.1016/j.jfa.2010.09.005},
  volume       = {261},
  year         = {2011},
}