Mathematical Scattering Theory: General TheoryPreliminary facts Basic concepts of scattering theory Further properties of the WO Scattering for relatively smooth perturbations The general setup in stationary scattering theory Scattering for perturbations of trace class type Properties of the scattering matrix (SM) The spectral shift function (SSF) and the trace formula |
Contents
| 5 | |
| 13 | |
Basic Concepts of Scattering Theory | 67 |
Further Properties of the WO | 97 |
Scattering for Relatively Smooth Perturbations | 113 |
The General Scheme in Stationary Scattering Theory | 153 |
Scattering for Perturbations of Trace Class Type | 187 |
Properties of the Scattering Matrix SM | 229 |
The Spectral Shift Function SSF and the Trace Formula | 265 |
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Common terms and phrases
a₁ absolutely continuous arbitrary assertion assumed assumptions Borel set bounded operator compact conditions of Theorem consider constructed converges COROLLARY corresponding decomposition defined definition denote direct integral eigenvalues element f equal to zero equation equivalent estimate existence f₁ finite full measure functions f G₁ H-smooth H₁ H₂ hence Hilbert space Hilbert-Schmidt operators Hölder continuous holds holomorphic I₁ inequality integral operator isometric kernel Lebesgue measure left-hand side Lemma limit Moreover multiplication norm obtain operator H operator-valued function pair proof of Theorem Proposition relation representation resolvent respect right-hand side Ro(z s-lim S₁ S₂ satisfied scattering matrix scattering operator scattering theory selfadjoint operator sesquilinear form singular smooth spectral spectral theorem spectrum stationary subspace suffices time-dependent trace class U₁ unitarily unitary operators verify W(Ho W₁ W₁(H W₁(Ho z₁ αλ Ηο ίε λεΛ λο μ₁
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