Lahiani, Raza (1982....).
Overview
Works:  1 works in 2 publications in 1 language and 2 library holdings 

Roles:  Author 
Publication Timeline
.
Most widely held works by
Raza Lahiani
Analyse harmonique sur certains groupes de Lie à croissance polynomiale by
Raza Lahiani(
Book
)
2 editions published in 2010 in French and held by 2 WorldCat member libraries worldwide
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 Kprime ideals of the Schwartz algebra. The passage to the Kprime 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 Kprime ideals
2 editions published in 2010 in French and held by 2 WorldCat member libraries worldwide
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 Kprime ideals of the Schwartz algebra. The passage to the Kprime 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 Kprime ideals
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Ludwig, Jean (1947....). Thesis advisor
 Université du Luxembourg Other Degree grantor
 Université de Metz Degree grantor
 Arnal, Didier (1946....). Opponent
 Olbrich, Martin (1963....). Other
 Pasquale, Angela Opponent
 MolitorBraun, Carine Opponent
 École doctorale IAEM Lorraine  Informatique, Automatique, Électronique  Électrotechnique, Mathématiques de Lorraine Other
 LMAM  Laboratoire de Mathémathiques et Applications de Metz  UMR 7122 (....2012) Other
Languages