Skip to main content

Distributions sphériques invariantes sur l'espace symétrique semi-simple et son c-dual

  • Chapter
  • First Online:
Non-Commutative Harmonic Analysis and Lie Groups

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1243))

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographie

  1. M.F. Atiyah, Characters of semi-simple Lie groups (lectures given in Oxford), Mathematical Institute, Oxford, 1976.

    Google Scholar 

  2. J. Faraut, Distributions sphériques sur les espaces hyperboliques, J. Math. Pures Appl., 58(1979), 369–444.

    MathSciNet  MATH  Google Scholar 

  3. J.Faraut, Analyse harmonique sur les paires de Guelfand et les espaces hyperboliques, Analyse Harmonique, (1983), 315–446.

    Google Scholar 

  4. J.Faraut, Analyse harmonique et fonctions speciales, Ecole d'été d'analyse harmonique de tunis, (1984).

    Google Scholar 

  5. M. Flensted-Jensen, Discrete series for semi-simple symmetric spaces, ANN. of Math., 111(1980), 253–311.

    Article  MathSciNet  MATH  Google Scholar 

  6. S.Helgason, Differential Geometry and symmetric spaces, Academic Press, 1962.

    Google Scholar 

  7. S.Helgason, Analysis on Lie groups and homogeneous spaces, Regional Conference series in Mathematics, Amer. Math. Soc. 14, 1972.

    Google Scholar 

  8. Harish-Chandra, The characters of semi-simple Lie groups, Trans. Amer. Math. Soc., 83(1956), 98–163.

    Article  MathSciNet  MATH  Google Scholar 

  9. Harish-Chandra, Some results on an invariant integral on a semi-simple Lie algebra, Ann. of Math., 80(1964), 551–593.

    Article  MathSciNet  MATH  Google Scholar 

  10. T. Hirai, Invariant eigendistributions of Laplace operators on real simple Lie groups I, Japan. J. Math., 39(1970), 1–68.

    MathSciNet  MATH  Google Scholar 

  11. T. Hirai, The Plancherel formula for SU(p,q), J. Math. Soc. Japan, 22(1970), 134–179.

    Article  MathSciNet  MATH  Google Scholar 

  12. T. Hirai, Invariant eigendistributions of Laplace operators on real simple Lie groups II, Japan.J.Math.New series, 2 (1976), 27–89.

    MathSciNet  MATH  Google Scholar 

  13. M. Kashiwara, The Riemann-Hilbert Problem for Holonomic Systems, Publ.RIMS,Kyoto Univ., 20(1984), 319–365.

    Article  MathSciNet  MATH  Google Scholar 

  14. O. Loos, Symmetric spaces, Vols.I–II, Benjamin, New York, 1969.

    Google Scholar 

  15. T. Oshima-T. Matsuki, Orbits on affine symmetric spaces under the action of the isotropic subgroup, J.Math.Soc.Japan, 32 (1980),399–414.

    Article  MathSciNet  MATH  Google Scholar 

  16. T. Oshima-T. Matsuki, A complete description of discrete series for semi-simple symmetric spaces, Advanced studies in Pure Math., 4(1984) 331–390.

    MathSciNet  MATH  Google Scholar 

  17. T. Oshima-J. Sekiguchi, Eigenspaces of invariant differential Operators on an affine symmetric space, Invent. Math., 57 (1980), 1–81.

    Article  MathSciNet  MATH  Google Scholar 

  18. T. Oshima-J. Sekiguchi, The Restricted Root System of a Semisimple Symmetric Pair, Advanced studies in Pure Math., 4 (1984), 433–497.

    MathSciNet  MATH  Google Scholar 

  19. S. Sano, Invariant spherical distributions and the Fourier inversion formula on GL(n,ℂ)/GL(n,ℝ), J.Math.Soc.Japan, 36 (1984), 191–219.

    Article  MathSciNet  MATH  Google Scholar 

  20. S. Sano-S. Aoki-S. Kato, A Note on Connection Formulas for Invariant Eigendistributions on Certain Semisimple Symmetric Spaces, Bull. of I.V.T., 14-A(1985), 99–108.

    MathSciNet  Google Scholar 

  21. S.Sano-N.Bopp, Distributions sphériques invariantes sur l'espace semi-simple symétrique Gc/GR, preprint.

    Google Scholar 

  22. S. Sano-J. Sekiguchi, The Plancherel formula for SL(2,C)/SL(2,R), Sci. Papers College Ged.Ed.Tokyo,30(1980), 93–105.

    MathSciNet  MATH  Google Scholar 

  23. M. Sugiura, Conjugate classes of Cartan subalgebras in real semi-simple Lie algebras, J.Math.Soc.Japan, 11(1959), 374–434.

    Article  MathSciNet  MATH  Google Scholar 

  24. M.Sugiura, Unitary representations and harmonic analysis Kodansha, Tokyo, 1975.

    Google Scholar 

  25. R. Takahashi, Sur les functions spheriques et la formule de Plancherel dans le groupe hyperbolique, Japan.J.Math., 31 (1961), 55–90.

    MathSciNet  MATH  Google Scholar 

  26. V.S.Varadarajan, Harmonic Analysis on real reductive groups, Lecture Notes in Math., 576, Springer Verlag, 1977.

    Google Scholar 

  27. G.Warner, Harmonic Analysis on semi-simple Lie groups, Vol. 1, 2, Springer Verlag, 1972.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jacques Carmona Patrick Delorme Michèle Vergne M.I.T.

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag

About this chapter

Cite this chapter

Sano, S. (1987). Distributions sphériques invariantes sur l'espace symétrique semi-simple et son c-dual. In: Carmona, J., Delorme, P., Vergne, M., M.I.T. (eds) Non-Commutative Harmonic Analysis and Lie Groups. Lecture Notes in Mathematics, vol 1243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073028

Download citation

  • DOI: https://doi.org/10.1007/BFb0073028

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17701-2

  • Online ISBN: 978-3-540-47775-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics