  Coordinate formalism on Hilbert manifolds developed in Kryukov is reviewed.
The results of 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 smooth solution by a
(functional) coordinate transformation. The results also suggest a way of using
generalized functions to solve nonlinear problems on Hilbert spaces.
