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
Creators:	Creators Email ORCID Kryukov, Alexey
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 15:10
Item ID:	508
Subjects:	Specific Sciences > Mathematics
Date:	December 2001
URI:	https://philsci-archive.pitt.edu/id/eprint/508

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