2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145095A 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 pagesFunctional Analysis46F30, 46F05, 46E10, 42A38text