Persistence of embedded eigenvalues

2010/08/12 by Shmuel Agmon, Agmon, Shmuel, Ira Herbst +3
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #math-ph #math.FA #math.MP #msc:81Q15

paper · pdf · doi:10.48550/arxiv.1008.2099

arxiv created 2011/03/15 · arxiv updated 2011/03/16

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 co-dimension m.

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