Coordinate formalism on abstract Hilbert space

Publication Year:
2001
Usage 178
Downloads 178
Repository URL:
http://philsci-archive.pitt.edu/id/eprint/508
Author(s):
Kryukov, Alexey
preprint description
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.