Asymptotic Expansions on Symmetric Spaces

  • Erik van den Ban
  • Henrik Schlichtkrull
Chapter
Part of the Progress in Mathematics book series (PM, volume 101)

Abstract

Let G/H be a semisimple symmetric space, where G is a connected semisimple real Lie group with an involution σ, and H is an open subgroup of the fix point group Gσ. Assume that G has finite center; then it is known that G has a σ-stable maximal compact subgroup K.

Keywords

Wallach 

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References

  1. [B87]
    Ban E.P. van den Asymptotic behaviour of matrix coefficients related to reductive symmetric spaces, Proc. Kon. Nederl. Akad. Wet. 90 (1987), 225–249.Google Scholar
  2. [BS87]
    Ban E.P. van den and H. Schlichtkrull, Asymptotic expansions and boundary values of eigenfunctions on Riemannian symmetric spaces, J. reine angew. Math. 380 (1987), 108–165.MathSciNetMATHGoogle Scholar
  3. [BS89]
    Ban E.P. van den and H. Schlichtkrull , Local boundary data of eigenf unctions on a Riemannian symmetric space, Invent. math. 98 (1989), 639–657.MathSciNetMATHCrossRefGoogle Scholar
  4. [CM82]
    Casselman, W. and D. Miličić, Asymptotic behaviour of matrix coefficients of admissible representations, Duke Math. J. 49 (1982), 869–930.MathSciNetMATHCrossRefGoogle Scholar
  5. [FOS88]
    Flensted-Jensen, M., T. Oshima and H. Schlichtkrull, Boundedness of certain unitarizable Harish-Chandra modules, Adv. Stud, in Pure Math. 14 (1988), 651–660.MathSciNetGoogle Scholar
  6. [HC60]
    Harish-Chandra, Differential equations and semisimple Lie groups, Collected Papers, vol. 3, Springer-Verlag, 1983, pp. 57–120.Google Scholar
  7. [S84]
    Schlichtkrull, H., Hyperfunctions and harmonic analysis on symmetric spaces, Birkhäuser, 1984.MATHCrossRefGoogle Scholar
  8. [W83]
    Wallach, N., Asymptotic expansions of generalized matrix entries of representations of real reductive groups, Lecture Notes in Math. 1024 (1983), 287–369.MathSciNetCrossRefGoogle Scholar
  9. [W88]
    Wallach, N., Real reductive groups, vol. 1, Academic Press, 1988.Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Erik van den Ban
    • 1
  • Henrik Schlichtkrull
    • 2
  1. 1.Department of MathematicsUniversity of UtrechtUtrechtThe Netherlands
  2. 2.Department of Mathematics and PhysicsThe Royal Veterinary and Agricultural UniversityFrederiksberg CDenmark

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