Persistence of embedded eigenvalues
Functional Analysis
2011-03-16 v2 Mathematical Physics
math.MP
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 < \infty 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 co-dimension m.
Keywords
Cite
@article{arxiv.1008.2099,
title = {Persistence of embedded eigenvalues},
author = {Shmuel Agmon and Ira Herbst and Sara Maad Sasane},
journal= {arXiv preprint arXiv:1008.2099},
year = {2011}
}