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Coordinate formalism on abstract Hilbert space

Kryukov, Alexey (2001) Coordinate formalism on abstract Hilbert space. [Preprint]

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    Abstract

    Coordinate formalism on Hilbert manifolds developed in \cite{Kryukov} is reviewed. The results of \cite{Kryukov} are applied to the simpliest case of a Hilbert manifold: the abstract Hilbert space. In particular, functional transformations preserving properties of various linear operators on Hilbert spaces are found. Any generalized solution of an arbitrary linear differential equation with constant coefficients is shown to be related to a regular solution by a (functional) coordinate transformation. The results also suggest a way of using generalized functions to solve nonlinear problems on Hilbert spaces.


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    Item Type: Preprint
    Keywords: Hilbert manifolds, generalized functions, partial differential equations
    Subjects: Specific Sciences > Mathematics
    Depositing User: Alexey Kryukov
    Date Deposited: 10 Dec 2001
    Last Modified: 07 Oct 2010 11:10
    Item ID: 508
    URI: http://philsci-archive.pitt.edu/id/eprint/508

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