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Perturbations of embedded eigenvalues for the planar bilaplacian

Derks, Gianne; Maad Sasane, Sara LU and Sandstede, Björn (2011) In Journal of Functional Analysis 260(2). p.340-398
Abstract
Operators on unbounded domains may acquire eigenvalues that are embedded in the essential spectrum. Determining the fate of these embedded eigenvalues under small perturbations of the underlying operator is a challenging task, and the persistence properties of such eigenvalues are linked intimately to the multiplicity of the essential spectrum. In this paper, we consider the planar bilaplacian with potential and show that the set of potentials for which an embedded eigenvalue persists is locally an infinite-dimensional manifold with infinite codimension in an appropriate space of potentials.
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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Embedded eigenvalues, Persistence, Perturbation, Bilaplacian
in
Journal of Functional Analysis
volume
260
issue
2
pages
59 pages
publisher
Elsevier
external identifiers
  • scopus:78049438054
ISSN
0022-1236
DOI
10.1016/j.jfa.2010.10.001
language
English
LU publication?
no
id
0fdc7dd4-6d5f-4f4d-a63f-68938af0da9d
date added to LUP
2017-02-08 13:39:58
date last changed
2017-03-13 12:39:16
@article{0fdc7dd4-6d5f-4f4d-a63f-68938af0da9d,
  abstract     = {Operators on unbounded domains may acquire eigenvalues that are embedded in the essential spectrum. Determining the fate of these embedded eigenvalues under small perturbations of the underlying operator is a challenging task, and the persistence properties of such eigenvalues are linked intimately to the multiplicity of the essential spectrum. In this paper, we consider the planar bilaplacian with potential and show that the set of potentials for which an embedded eigenvalue persists is locally an infinite-dimensional manifold with infinite codimension in an appropriate space of potentials.},
  author       = {Derks, Gianne and Maad Sasane, Sara and Sandstede, Björn},
  issn         = {0022-1236},
  keyword      = {Embedded eigenvalues,Persistence,Perturbation,Bilaplacian},
  language     = {eng},
  number       = {2},
  pages        = {340--398},
  publisher    = {Elsevier},
  series       = {Journal of Functional Analysis},
  title        = {Perturbations of embedded eigenvalues for the planar bilaplacian},
  url          = {http://dx.doi.org/10.1016/j.jfa.2010.10.001},
  volume       = {260},
  year         = {2011},
}