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    EXISTENCE AND COMPLETENESS OF WAVE OPERATORS IN TWO HILBERT SPACES

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    Date
    1984
    Author
    ALTABET, MERYL J.
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    Abstract
    In this thesis we consider an unperturbed self-adjoint operator H(,0) on a Hilbert space H(,0), the operators A, B mapping H(,0) to the Hilbert space K, and J a bounded linear operator mapping the Hilbert space H(,0) to the Hilbert space H.;Our first objective is to give conditions under which there exists a perturbed self-adjoint operator H such that R(z)J - JR(,0)(z) = -(BJ('*)R(z))*AR(,0)(z) and HJ(R-HOOK)J(H(,0) + B('*)A). We prove the existence of the operator H by actually constructing its resolvent R(z).(').;Our next objective is to consider two specific operators H(,0), the momentum operator and the kinetic energy operator, and to give examples of A, B, J for which the main conclusions of scattering theory hold. In obtaining conditions for the existence and completeness of the wave operator, we use a combination of time dependent and stationary methods.
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    https://ezproxy.yu.edu/login?url=http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:8502685
    https://hdl.handle.net/20.500.12202/2968
    Citation
    Source: Dissertation Abstracts International, Volume: 45-12, Section: B, page: 3836.
    *This is constructed from limited available data and may be imprecise.
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    • Mathematical Sciences Dissertations [146]

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