Persistence of embedded eigenvalues

Shmuel Agmon, Ira Herbst, Sara Maad Sasane

Published 2010-08-12, updated 2011-03-15Version 2

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.