English

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}
}
R2 v1 2026-06-21T15:59:56.483Z