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1 CRREF - Centre de recherches et de ressources en éducation et formation 2 AOC - Analyse Optimisation Controle

Abstract : 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}′}, the space of rapidly generalized distributions which is the Fourier image of G {τ}.

Keywords : Rapidly decreasing distributions Fourier Transform Temperate distributions Fourier Transform. Colombeau generalized functions Colombeau temperate generalized functions Rapidly decreasing functions Schwartz distributions

Author: Antoine Delcroix -

Source: https://hal.archives-ouvertes.fr/


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