The Birman-schwinger Principle on the Essential Spectrum
نویسنده
چکیده
Let H0 and H be self-adjoint operators in a Hilbert space. We consider the spectral projections of H0 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 H0, H.
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تاریخ انتشار 2010