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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absolutely continuous according to Theorem apply arbitrary assertion assumed assumptions Borel set bounded operator coincide compact conditions of Theorem consider constructed converges COROLLARY corresponding decomposition definition denote Det(I differentiable direct integral eigenvalues equal to zero equation equivalent estimate example existence finite finite-dimensional follows directly full measure functions ƒ G₁ H and H H-smooth H₁ H₂ hence Hilbert space Hilbert-Schmidt Hilbert-Schmidt operators Hölder continuous holds holomorphic inequality integral operator isometric kernel L₂(R Lebesgue measure left-hand side limit Moreover multiplication norm obtain operator H operator-valued function pair H proof of Theorem Proposition relation respect right-hand side s-lim S₁ satisfied scattering matrix scattering operator scattering theory selfadjoint operator sesquilinear form set of full singular smooth spectral spectral theorem spectrum subspace time-dependent trace class trace class perturbations U₁ unitarily unitary operators weak
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