Perturbations of embedded eigenvalues for the planar bilaplacian
(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
- Derks, Gianne ; Maad Sasane, Sara LU and Sandstede, Björn
- organization
- publishing date
- 2011
- 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
- 2022-01-30 17:48:30
@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}},
keywords = {{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}},
doi = {{10.1016/j.jfa.2010.10.001}},
volume = {{260}},
year = {{2011}},
}