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manuscripta mathematica

, Volume 29, Issue 2–4, pp 249–276 | Cite as

On the Plancherel measure for linear Lie groups of rank one

  • Roberto J. Miatello
Article

Abstract

In this paper we find a very explicit, simple form for the Plancherel measure for rank one, linear simple groups, including the normalizing constant.

Keywords

Simple Form Number Theory Algebraic Geometry Simple Group Topological Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    BOURBAKI: Elements de Mathematique, Groupes et algébres de Lie, Chap. 4-6, Paris, Hermann (1968)Google Scholar
  2. [2]
    KNAPP, A. and STEIN, E.: Intertwining operators for semi-simple groups, Ann. of Math. 93, 489–578 (1971)Google Scholar
  3. [3]
    MIATELLO, R.: The Minakshisundaram-Pleijel coefficients for the vector valued heat kernel on compact. locally symmetric spaces of negative curvature. To appear in Transactions of the A.M.S.Google Scholar
  4. [4]
    OKAMOTO, K.: On the Plancherel formulas for some types of simple Lie groups, Osaka J. Math. 2, 247–282 (1965)Google Scholar
  5. [5]
    RADER, C.: Invariant polynomials and spherical functions. To appear in Boletim da Sociedade Brasileira de MatemáticaGoogle Scholar
  6. [6]
    WALLACH, N. R.: Harmonic Analysis on homogeneous spaces, 1st edn, New York, M. Dekker (1973)Google Scholar
  7. [7]
    WARNER, G.: Harmonic Analysis on semi-simple Lie groups I and II, 1st edition, New York, Springer-Verlag (1972)Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Roberto J. Miatello
    • 1
  1. 1.Departmento de MatemáticaUniversidade Federal de PernambucoRecifeBrasil

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