A new approach to temperate generalized Colombeau functions

Abstract

A new approach to the algebra G? of temperate nonlinear generalized functions is proposed, in which G? is based on the space OM 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?. This is illustrated by the natural introduction of a regularity theory in G?, of the Fourier transform, with the definition of GO'C, the space of rapidly generalized distributions which is the Fourier image of G?.