Operator theoretic methods for the eigenvalue counting function in spectral gaps

Details Operator theoretic methods for the eigenvalue counting function in spectral gaps Operator theoretic methods for the eigenvalue counting function in spectral gaps

2008-09-25

arxiv.org/abs/0809.4365v1

Mathematics

Spectral Theory

Latex, 25 pages

Scientific paper

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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