Contributions to Fourier analysis in Colombeau algebra
Contributions to Fourier analysis in Colombeau algebra
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Date
2011-10-30
Auteurs
Saidi Tayeb
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Éditeur
Université Oran1 Ahmed Ben Bella
Résumé
The Present work is a contribution to generalized functions theory founded by G. F. Colom beau. This theory, whose provide a solution to the problem of distributions multiplication, does not stop to be developed in deferent .ends of mathematics generalizing, in this way, a lot of classical results. Our work, although is humble, contributes particularly to the Fourier analysis in the frame work of Colom beau generalized functions. In the .rest chapter, we recall the basic notions of generalized functions theory. In the second chapter, which is our .rest contribution, we give two characterizations of rapidly decreasing generalized functions, one of them uses the Fourier transformation. The third chapter represents our second contribution, it introduces basic elements for devil- opting a micro local analysis in the context of R-regularity of Colom beau generalized function.
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Mots-clés
Schwartz space, Rapidly decreasing generalized functions, Colom beau algebra, Generalized functions, Wave front set, Micro local analysis, Product of distributions