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< 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.
Original language | English |
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Pages (from-to) | 451-477 |
Number of pages | 27 |
Journal | Journal of Functional Analysis |
Volume | 261 |
Issue number | 2 |
DOIs | |
State | Published - 15 Jul 2011 |
Keywords
- Embedded eigenvalues
- Perturbation