Éditeur(s) : HAL CCSDElsevier Résumé : International audience In analogy to the classical Schwartz kernel theorem, we show that a large class of linear mappings admits integral kernels in the framework of Colombeau generalized functions. To do this, we introduce new spaces of generalized functions with slow growth and the corresponding adapted linear mappings. Finally, we show that, in some sense, Schwartz’ result is contained in our main theorem. ISSN: 0022-247X
Éditeur(s) : HAL CCSDDepartment of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad Résumé : International audience We present some remarks about the embedding of spaces of Schwartz distributions into spaces of Colombeau generalized functions. Following ideas of M. Nedeljkov et alii, we recall how a good choice of compactly supported mollifiers allows to perform globally the embedding of D' () into G (). We show that this embedding is equal to the one obtained with local and sheaf arguments by M. Grosser et alii, this giving various equivalent technics to embed D'() into G (). ISSN: 1450-5444
Éditeur(s) : HAL CCSD Résumé : Prelimary version - 13 pages. International audience 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}. Publ. Inst.Math. (Beograd) (N.S.)
Éditeur(s) : HAL CCSDAmerican Mathematical Society Résumé : International audience A topological description of various generalized function algebras over corresponding basic locally convex algebras is given. The framework consists of algebras of sequences with appropriate ultra( pseudo)metrics defined by sequences of exponential weights. Such an algebra with embedded Dirac's delta distribution induces discrete topology on the basic space. This result is in analogy to Schwartz' impossibility result concerning multiplication of distributions. ISSN: 0002-9939
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