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Operator Theoretic Methods for the Eigenvalue Counting Function in Spectral Gaps

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Original languageEnglish
Pages (from-to)793 - 822
Number of pages30
JournalAnnales Henri Poincare
Issue number4
PublishedJul 2009

King's Authors


Using the notion of spectral flow, we suggest a simple approach to various asymptotic problems involving eigenvalues in the gaps of the essential spectrum of self-adjoint operators. Our approach employs some elements of the theory of the spectral shift function. Using this approach, we provide generalisations and streamlined proofs of two results in this area already existing in the literature. We also give a new proof of the generalised Birman-Schwinger principle.

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