Titlebook: C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians; Werner O. Amrein,Anne Boutet Monvel,Vladimir Georg Book 1996 Bir

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Some Examples of ,,-Groups, Section 1.2) two .-parameter groups acting in .., namely {..} and {..}. If the Banach space . is invariant under one of these groups, one may define the associated Sobolev and Besov scales according to the theory of Chapter 3. This situation is described in Section 4.1. In Section 1.2 we also intro

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Unitary Representations and Regularity for Self-adjoint Operators,esentations . of ?. is a very well understood classical subject and will not be presented here. However we mention that a .-dimensional version of Stone’s theorem states that there is a unique spectral measure . on ?. such that . and this allows one to extend the functional calculus which we already

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The Conjugate Operator Method,owever, for certain vectors . ∈ ., the function ., which is defined and holomorphic for . outside the spectrum of ., could have a limit as . converges to λ from the upper or lower half-plane (these two limits will be different in general). If this happens for sufficiently many ., one can infer resul

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An Algebraic Framework for the Many-Body Problem,annel” is used here in a rather vague sense: we are thinking of systems consisting of a (large, but finite) number of components which could interact in a complicated way but could also behave independently (i.e. the interaction between some components could be turned off). So, to the “total hamilto

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