The Birman-Schwinger principle on the essential spectrum

Details The Birman-Schwinger principle on the essential spectrum The Birman-Schwinger principle on the essential spectrum

2009-11-11

arxiv.org/abs/0911.2134v1

Mathematics

Spectral Theory

Latex, 24 pages

Scientific paper

Let $H_0$ and $H$ be self-adjoint operators in a Hilbert space. We consider the spectral projections of $H_0$ and $H$ corresponding to a semi-infinite interval of the real line. We discuss the index of this pair of spectral projections and prove an identity which extends the Birman-Schwinger principle onto the essential spectrum. We also relate this index to the spectrum of the scattering matrix for the pair $H_0$, $H$.

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