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arXiv · 0809.4365

Operator theoretic methods for the eigenvalue counting function in spectral gaps

Alexander Pushnitski
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Abstract

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 uses some elements of the spectral shift function theory. 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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Alexander Pushnitski. 2008-09-25. Operator theoretic methods for the eigenvalue counting function in spectral gaps. https://doi.org/10.1007/s00023-009-0422-z

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