Mémoires de Fin d’Etudes
Etablissement
Université d’Oran1 - Ahmed Ben Bella
Affiliation
Département de Mathématique
Auteur
SAIDI, Tayeb
Directeur de thèse
BOUZAR Chikh (Professeur)
Filière
Mathématiques
Diplôme
Doctorat
Titre
Contributions to fourier analysis in colombeau algebra
Mots clés
Schwartz space; Rapidly decreasing generalized functions; Colombeau algebra; Generalized functions; Wave front set; Microlocal analysis; Product of distributions
Résumé
The Present work is a contribution to generalized functions theory founded by G. F. Colombeau. This theory, whose provide a solution to the problem of distributions multiplication, does not stop to be developed in di¤erent .elds 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 Colombeau generalized functions. In the .rst chapter, we recall the basic notions of generalized functions theory. In the second chapter, which is our .rst 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 devel- oping a microlocal analysis in the context of R-regularity of Colombeau generalized function.
Date de soutenance
2011
Cote
TH3554
Pagination
65F.
Format
30 cm
Notes
BIBLIOG.
Statut
Soutenue