A new approach to temperate generalized functions
Abstract
Description
A new approach to the algebra G_τ of temperate nonlinear generalized functions is proposed, in which G_τ is based on the space O_{M} endowed with is natural topology in contrary to previous constructions. Thus, this construction fits perfectly in the general scheme of construction of Colombeau type algebras and reveals better properties of G_τ. This is illustrated by the natural introduction of a regularity theory in G_τ, of the Fourier transform, with the definition of G_{O_{C prime}}, the space of rapidly generalized distributions which is the Fourier image of G_τ.
Prelimary version - 13 pages
Prelimary version - 13 pages