Download PDF - Hull-minimal ideals in the Schwartz algebra of the Heisenberg groupAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Hull-minimal ideals in the Schwartz algebra of the Heisenberg group

Authors 1

Affiliations

  1. Université de Metz, Département de Mathématiques, Ile du Saulcy, 57045 Metz Cedex 01, France

Abstract

For every closed subset C in the dual space Ĥn of the Heisenberg group Hn we describe via the Fourier transform the elements of the hull-minimal ideal j(C) of the Schwartz algebra S(Hn) and we show that in general for two closed subsets C1,C2 of Ĥn the product of j(C1) and j(C2) is different from j(C1∩C2).

Bibliography

  1. [BD] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, 1973.
  2. [CG] L. Corwin and F. P. Greenleaf, Representations of Nilpotent Lie Groups and Their Applications Cambridge Univ. Press, 1990.
  3. [Di1] J. Dixmier, Les C*-algèbres et leurs représentations, Gauthier-Villars, 1969.
  4. [Di2] J. Dixmier, Opérateurs de rang fini dans les représentations unitaires, Inst. Hautes Etudes Sci. Publ. Math. 6 (1960), 305-317.
  5. [FO] G. Folland, Harmonic Analysis in Phase Space, Princeton Univ. Press, 1989.
  6. [FS] G. Folland and E. Stein, Hardy Spaces on Homogeneous Groups, Math. Notes 28, Princeton Univ. Press, 1982.
  7. [Hu] A. Hulanicki, A functional calculus for Rockland oerators on nilpotent Lie groups, Studia Math. 78 (1984), 253-266.
  8. [Lu1] J. Ludwig, Polynomial growth and ideals in group algebras, Manuscripta Math. 30 (1980), 215-221.
  9. [Lu2] J. Ludwig, Minimal C*-dense ideals and algebraically irreducible representations of the Schwartz-algebra of a nilpotent Lie group, in: Harmonic Analysis, Springer, 1987, 209-217.
  10. [Lu3] J. Ludwig, Topologically irreducible of the Schwartz-algebra a nilpotent Lie group, Arch. Math. (Basel) 54 (1990), 284-292.
  11. [LM] J. Ludwig et C. Molitor-Braun, L'algèbre de Schwartz d'un groupe de Lie nilpotent, Travaux de Mathématiques Publications du C.U. Luxembourg, 1996.
  12. [LRS] J. Ludwig, G. Rosenbaum and J. Samuel, The elements of bounded trace in the C*-algebra of a nilpotent Lie group, Invent. Math. 83 (1986), 167-190.
  13. [LZ] J. Ludwig and H. Zahir, On the nilpotent Fourier transform, Lett. math. Phys. 30, (1994), 23-34.
  14. [Rei] H. Reiter, Classical Harmonic Analysis and Locally Compact Groups, Oxford Math. Monographs, Oxford Univ. Press, 1968.
Studia Mathematica
1998/130/1
Export to PBN, Opens in new tab
Pages:
77-98
Main language of publication
English
Received
1997-03-10
Published
1998
Exact and natural sciences