Coordinate formalism on Hilbert manifolds

Kryukov, Alexey (2001) Coordinate formalism on Hilbert manifolds.

Abstract

Infinite-dimensional manifolds modelled on arbitrary Hilbert spaces of functions
are considered. It is shown that changes in model rather than
changes of charts within the same model make coordinate
formalisms on finite and infinite-dimensional manifolds deeply similar. In this context the
infinite-dimensional counterparts of simple notions
such as basis, dual basis, orthogonal basis, etc. are shown to be closely related to
the choice of a model.
It is also shown that in this formalism a single tensor equation on an infinite-dimensional
manifold produces a family of functional equations on different spaces of functions.