We present a general spectral stability theorem which allows to compare the eigenvalues of two non-negative self-adjoint operators with compact resolvents acting on different Hilbert spaces. This theorem is based on the notion of transition operator which is introduced. Examples and applications to domain perturbation problems are discussed.
Spectral stability of nonnegative self-adjoint operators
BURENKOV, VICTOR;LAMBERTI, PIER DOMENICO
2005
Abstract
We present a general spectral stability theorem which allows to compare the eigenvalues of two non-negative self-adjoint operators with compact resolvents acting on different Hilbert spaces. This theorem is based on the notion of transition operator which is introduced. Examples and applications to domain perturbation problems are discussed.
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