Télécharger La thèse :

Titre: Contributions to Fourier analysis in Colombeau algebra

Domaine: Mathématiques informatique (MI)

Filière: Mathématique

Option: Analyse Mathématique

Auteur: Saidi Tayeb

Soutenu (e) le: 30/10/2011

Sous la direction de: BOUZAR Chikh, Professeur, Université d’Oran

Le président du jury : BEKKAR Mohamed, Professeur, Université d’Oran

Examinateur1: MESSIRDI Bekkai, Professeur, Université d’Oran

Examinateur2: BOUCHEKIF Mohamed, Professeur, Université de Tlemcen

Examinateur3: BENCHOHRA Mouffak, Professeur, Université de Sidi Bel Abbes

Examinateur4: MECHAB Mustapha, Professeur, Université de Sidi Bel Abbes


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.

Mots clefs: Schwartz space; Rapidly decreasing generalized functions; Colom beau algebra; Generalized functions; Wave front set; Micro local analysis; Product of distributions

Publications associées à la thèse

Article 2857:

Titre: Communications of the Korean Mathematical Society

Revue: Characterizations of rapidly decreasing generalized functions

Référence: Vol. 25, No. 3, 2010, p. 391-404 . 2010

Date: 2010

Publications associées à la thèse

Article 2858:

Titre: Integral Transform and Special functions

Revue: Fourier analysis of generalized functions

Référence: Vol. 22, No. 4-5, 2011, p. 337-344 . 2011

Date: 2011