The Birman–Schwinger principle on the essential spectrum
Copyright policy )The Birman–Schwinger principle on the essential spectrum
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 $H_0$, $H$.
Latex, 24 pages
- King's College London United Kingdom
- Kings College London, University of London United Kingdom
Birman-Schwinger principle, essential spectrum, spectral projections, Birman–Schwinger principle, Perturbation theory of linear operators, Spectral projections, Scattering theory of linear operators, 35P25, 47B25, 47F05, 510, Functional Analysis (math.FA), Mathematics - Spectral Theory, Mathematics - Functional Analysis, 47A40, FOS: Mathematics, Scattering matrix, (Semi-) Fredholm operators; index theories, 47A40; 35P25, 47B25, 47F05, Essential spectrum, Spectral Theory (math.SP), Analysis, scattering matrix
Birman-Schwinger principle, essential spectrum, spectral projections, Birman–Schwinger principle, Perturbation theory of linear operators, Spectral projections, Scattering theory of linear operators, 35P25, 47B25, 47F05, 510, Functional Analysis (math.FA), Mathematics - Spectral Theory, Mathematics - Functional Analysis, 47A40, FOS: Mathematics, Scattering matrix, (Semi-) Fredholm operators; index theories, 47A40; 35P25, 47B25, 47F05, Essential spectrum, Spectral Theory (math.SP), Analysis, scattering matrix
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