Functional Analysis and Its Applications

, Volume 27, Issue 1, pp 21–27 | Cite as

Harmonic analysis and the global exponential map for compact Lie groups

  • A. H. Dooley
  • N. J. Wildberger


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  1. 1.
    F. A. Berezin and I. M. Gelfand, “Some remarks on the theory of spherical functions on symmetric Riemannian manifolds,” Trudy Mosk. Mat. Obshch.,5, 311–351 (1956).Google Scholar
  2. 2.
    A. H. Dooley, J. Repka, and N. J. Wildberger, “Sums of adjoint orbits,” (to appear).Google Scholar
  3. 3.
    M. Duflo, “Opérateurs différentiels bi-invariants sur un groupe de Lie,” Ann. Sci. Ecole Norm. Sup.,10, 265–288 (1977).Google Scholar
  4. 4.
    I. Frenkel, Personal communication.Google Scholar
  5. 5.
    M. Kashiwara and M. Vergne, “The Campbell—Hausdorff formula and invariant hyperfunctions,” Invent. Math.,47, 249–272 (1978).Google Scholar
  6. 6.
    A. A. Kirillov, “Characters of unitary representations of Lie groups. Reduction theorems,” Funkts. Anal. Prilozhen.,3, No. 1, 36–47 (1969).Google Scholar
  7. 7.
    D. L. Ragozin, “Central measures on compact semi-simple Lie groups,” J. Functional Anal.,10, 212–229 (1972).Google Scholar
  8. 8.
    R. Thompson, “Author vs referee: A case history for middle level mathematicians,” Amer. Math. Monthly,90, No. 10, 661–668 (1983).Google Scholar
  9. 9.
    V. S. Varadarajan, Harmonic Analysis on Real Reductive Groups, LNM 576, Springer-Verlag, Berlin (1977).Google Scholar
  10. 10.
    M. Vergne, “A Plancherel formula without group representations,” in: Operator Algebras and Group Representations, II, Neptune (1980), pp. 217–226.Google Scholar
  11. 11.
    N. J. Wildberger, “On a relationship between adjoint orbits and conjugacy classes of a Lie group,” Canad. Math. Bull.,33, No. 3, 297–304 (1990).Google Scholar
  12. 12.
    N. J. Wildberger, “Hypergroups and harmonic analysis,” Proc. Centre Math. Anal. (ANU),29, 238–253 (1992).Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • A. H. Dooley
  • N. J. Wildberger

There are no affiliations available

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