|
Q.U.P. and Paley-Wiener properties of unimodular, especially nilpotent, Lie groups
Author(s):
Didier
Arnal;
Jean
Ludwig
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1071-1080.
MSC (1991):
Primary 43A30
MathSciNet review:
1353372
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We give a new proof of a weak Paley-Wiener theorem for nilpotent Lie groups due to Lipsman and Rosenberg and we introduce a general notion of Q.U.P for any unimodular locally compact group.
References:
- [Amr,Ber]
- W. O. Amrein and A. M. Berthier, On support properties of
 -functions and their Fourier transforms, J. Funct. Anal. 24 (1977), 258-267. MR 57:1013 - [Arn,Cor]
- D. Arnal and J. C. Cortet,
 -product in the method of orbits for nilpotent Lie groups, J. Geom. Phys. 2(2), (1985), 85-116. MR 88a:22017 - [Arn,Gut]
- D. Arnal and S. Gutt, Décomposition de
 et transformation de Fourier adaptée pour un groupe de Lie nilpotent, C. R. Acad. Sci. Paris, t. 306, Série I, (1988), 25-28. MR 88m:22015 - [Ben]
- M. Benedicks, On Fourier transforms of functions supported on sets of finite Lebesgue measure, J. Math. Anal. Appl. 106 (1985), 180-183. MR 86f:43006
- [Cor,Gre]
- L. Corwin, F. P. Greenleaf, Representations of nilpotent Lie groups and their applications Part 1: Basic theory and examples, Cambridge studies in advanced mathematics 18 (1990). MR 92b:22007
- [Cow,Pri,Sit]
- M. Cowling, J. F. Price and A. Sitaram, A qualitative uncertainty principle for semisimple Lie groups, J. Austral. Math. Soc. (Ser. A) 35 (1988), 127-132. MR 89d:43005
- [Dix(1)]
- J. Dixmier, Les
 -Algèbres et leurs Représentations, Gauthier-Villars (1969). MR 39:7442 - [Dix(2)]
- J. Dixmier, Opérateurs de rang fini dans les représentations unitaires. Publ. Math. IHES 6 (1960), 13-25. MR 25:149
- [Ech,Kan,Kum]
- S. Echterhoff, E. Kaniuth and A. Kumar, A qualitative uncertainty principle for certain locally compact groups, Forum Math. 3 (1991) 355-369. MR 93a:43005
- [Mat,Szu]
- T. Matolcsi and J. Szücs, Intersection des mesures spectrales conjuguées, C. R. Acad. Sci. Paris Série A. 277 (1973), 841-843. MR 48:4804
- [Gar]
- G. Garimella, Un théorème de Paley-Wiener pour les groupes de Lie nilpotents, preprint (1995).
- [Hog]
- J. A. Hogan, A qualitative Uncertainty Principle For Unimodular Groups of Type I, Trans. Amer. Math. Soc. 330 (1993), 587-593. MR 94b:43003
- [Lip,Ros]
- R. L. Lipsman and J. Rosenberg, The behavior of Fourier Transforms For Nilpotent Lie groups, preprint 1994.
- [Lud]
- J. Ludwig, Good ideals in the group algebra of a nilpotent Lie group, Math. Z. 161 (1983), 195-210.
- [Lud,Zah]
- J. Ludwig and H. Zahir, On the nilpotent
 -Fourier Transform, Lett. Math. Phys. 30 (1994), 23-34. MR 94k:22017 - [Mos]
- J. D. Moss, Jr., A Paley-Wiener Theorem for selected nilpotent Lie groups, J. Funct. Anal. 114 (1993), 395-411. MR 94e:22017
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (1991):
43A30
Retrieve articles in all Journals with
MSC (1991):
43A30
Additional Information:
Didier
Arnal
Affiliation:
Département de Mathématiques, Université de Metz, Laboratoire Méthodes Mathé- matiques pour l'Analyse des Systèmes, URA CNRS 399, Ile du Saulcy, 57045 Metz cedex, France
Email:
arnal@poncelet.univ-metz.fr
Jean
Ludwig
Affiliation:
Département de Mathématiques, Université de Metz, Laboratoire Méthodes Mathé- matiques pour l'Analyse des Systèmes, URA CNRS 399, Ile du Saulcy, 57045 Metz cedex, France
Email:
ludwig@poncelet.univ-metz.fr
DOI:
10.1090/S0002-9939-97-03608-3
PII:
S 0002-9939(97)03608-3
Received by editor(s):
June 12, 1995
Received by editor(s) in revised form:
September 21, 1995
Communicated by:
Roe Goodman
Copyright of article:
Copyright
1997,
American Mathematical Society
|
