Skip to main content
SpringerLink
Log in

Zentrale Distributionen auf nilpotenten Liegruppen

Central distributions on nilpotent Lie groups

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

We contribute some results to the following question discussed in several papers ([3], [9], [12]): To what extent the characters of the irreducible representations of a nilpotent Lie groupN determine all central tempered distributions onN. A hereditary property is proved, which enables us to give a negative answer for a large class of nilpotent Lie groups. However, we give a positive answer for a certain series of two-step nilpotent groups. Furthermore, proving a generalisation of the Schwartz Kernel Theorem we decide the question specially for all groups of dimension<5.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literatur

  1. Bourbaki, N.: Intégration. Chap. VI. Paris: Hermann. 1959.

    Google Scholar 

  2. Dixmier, J.: Sur les représentations unitaires des groupes de Lie nilpotents III. Canad. J. Math.10, 321–348 (1958).

    Google Scholar 

  3. Dixmier, J.: Sur les distributions invariantes par un groupe nilpotent. C. R. Acad. Sci., Paris, Sér. A285, 7–10 (1977).

    Google Scholar 

  4. Dixmier, J.: Sur la méthode des orbites. In: Non-Commutative Harmonic Analysis (Carmona, J., Vergne, M., eds.), pp. 42–63. Lecture Notes Math. 728. Berlin-Heidelberg-New York: Springer. 1979.

    Google Scholar 

  5. Felix, R.: Zerlegung von Distributionen, die unter einer unipotenten Gruppenoperation invariant sind. Comment. Math. Helv.55, 528–546 (1980).

    Google Scholar 

  6. Felix, R.: Das Syntheseproblem für invariante Distributionen. Invent. Math.65, 85–96 (1981).

    Google Scholar 

  7. Glimm, J.: Locally compact transformation groups. Trans. Amer. Math. Soc.101, 124–138 (1961).

    Google Scholar 

  8. Helgason, S.: The Radon Transform. Progress Math. 5. Boston-Basel-Stuttgart: Birkhäuser. 1980.

    Google Scholar 

  9. Herz, C.: Invariant distributions. Harmonic Analysis in Euclidean Spaces. Proc. Williamstown, Mass. 1978, pp. 361–373. Proc. Symp. Pure Math. 35, Part 2. Providence, R. I.: Amer. Math. Soc. 1979.

    Google Scholar 

  10. Köthe, G.: Topologische lineare Räume I. Berlin-Göttingen-Heidelberg: Springer. 1960.

    Google Scholar 

  11. Pukanszky, L.: Leçons sur les représentations des groupes. Paris: Dunod. 1967.

    Google Scholar 

  12. Rothschild, L.P., Wolf, J.A.: Eigendistribution Expansions on Heisenberg Groups. Indiana Univ. Math. J.25, 753–762 (1976).

    Google Scholar 

  13. Schwartz, L.: Espace de fonctions différentiables à valeurs vectorielles. J. Anal. Math.4, 88–148 (1954).

    Google Scholar 

  14. Schwartz, L.: Théorie des distributions à valeurs vectorielles. I. Ann. Inst. Fourier7, 1–141(1957).

    Google Scholar 

  15. Tengstrand, A.: Distributions invariant under an orthogonal group of arbitrary signature. Math. Scand.8, 201–218 (1960).

    Google Scholar 

  16. Trèves, F.: Topological Vector Spaces, Distribution and Kernels. New York: Academic Press. 1967.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Mathematik, Technische Universität, Postfach 20 2420, D-8000, München, Bundesrepublik Deutschland

    Rainer Felix

Authors
  1. Rainer Felix
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Felix, R. Zentrale Distributionen auf nilpotenten Liegruppen. Monatshefte für Mathematik 94, 91–101 (1982). https://doi.org/10.1007/BF01301927

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01301927

Search

Navigation