Persistence of embedded eigenvalues
(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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https://lup.lub.lu.se/record/0679744b-5655-4ff2-89c5-a76abee660ca
- author
- Agmon, Shmuel ; Herbst, Ira and Maad Sasane, Sara LU
- organization
- publishing date
- 2011
- 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<∞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.}}, 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}}, }