Perturbations of embedded eigenvalues for the planar bilaplacian
Derks, G, Maad Sasane, S and Sandstede, B (2011) Perturbations of embedded eigenvalues for the planar bilaplacian Journal of Functional Analysis, 260 (2). 340 - 398. ISSN 0022-1236
plane_radial.pdf - Accepted Version
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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.
|Additional Information:||NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Functional Analysis, 260(2), January 2011, DOI 10.1016/j.jfa.2010.10.001.|
|Divisions:||Faculty of Engineering and Physical Sciences > Mathematics|
|Depositing User:||Symplectic Elements|
|Date Deposited:||25 Jan 2012 17:02|
|Last Modified:||23 Sep 2013 18:59|
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