Analyse harmonique sur certains groupes de Lie à croissance polynomiale

Abstract : The first part of this thesis is devoted to the study of the existence of a smooth family of intertwining operators between two different families of equivalent representations and their effect on the retract theory. The second issue of this thesis is the retract theory. Let K be a compact Lie subgroup of Aut(N), acting smoothly on N. Then we construct a retract for the induced representations obtained by Vergne polarizations in the generic case and we transpose it to other choices of polarizations. We use the theory developed in the first part. In the third part, we characterize K-prime ideals of the Schwartz algebra. The passage to the K-prime ideals of the group algebra is then realized via the retract theory developed in the second part and the density property of the schwartz functions, at least in the generic case and in the character case. Finally, we study the action of SO(4) on F(4), specially the non genric case where F(4) denotes the free nilpotent Lie group of step 2 with 4 generators. We prove the fourier inversion theorem in the non genric case and we characterize all the K-prime ideals
Document type :
Theses
Complete list of metadatas

Cited literature [34 references]  Display  Hide  Download

https://hal.univ-lorraine.fr/tel-01752676
Contributor : Thèses Ul <>
Submitted on : Thursday, March 29, 2018 - 1:54:12 PM
Last modification on : Monday, April 16, 2018 - 10:42:42 AM

File

Lahiani.Raza.SMZ1001.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : tel-01752676, version 1

Collections

Citation

Raza Lahiani. Analyse harmonique sur certains groupes de Lie à croissance polynomiale. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 2010. Français. ⟨NNT : 2010METZ001S⟩. ⟨tel-01752676⟩

Share

Metrics

Record views

21

Files downloads

14