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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
; and
organization
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
2022-01-30 17:48:29
@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}},
  keywords     = {{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}},
  doi          = {{10.1016/j.jfa.2010.09.005}},
  volume       = {{261}},
  year         = {{2011}},
}