Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Cramér theorem on symmetric spaces of noncompact type

  • 28 Accesses

  • 9 Citations

Abstract

We prove the Cramér theorem forK-invariant Gaussian measures on irreducible symmetric spacesX=G/K withG semisimple noncompact. To do this we use a kind of Abel transform ofK-invariant measures onX.

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

References

  1. 1.

    Faraut, J. (1983). Analyse harmonique sur les paires de Guelfand et les espaces hyperboliques,Analyse Harmonique, les Cours du C.I.M.P.A., Nice, pp. 315–446.

  2. 2.

    Feller, W. (1966).An Introduction to Probability Theory, Volume II, Wiley, New York.

  3. 3.

    Graczyk, P. (1992). A central limit theorem on the space of positive definite symmetric matrices,Ann. Inst. Fourier, Vol. 42 (to appear).

  4. 4.

    Graczyk, P. Dispersions and a central limit theorem on symmetric spaces,Bull. Sc. Math. (to appear).

  5. 5.

    Heyer, H. (1977).Probability Measures on Locally, Compact Groups, Springer Verlag, Berlin.

  6. 6.

    Helgason, S. (1970). A duality for symmetric spaces with applications to group representations,Advances in Mathematics,5, 1–154.

  7. 7.

    Helgason, S. (1984).Groups and Geometric Analysis, Academic Press, New York.

  8. 8.

    Letac, G. (1981). Problèmes classiques de probabilité sur un couple de Gelfand, Analytical methods in probability theory,Proceedings, Oberwolfach 1980, LNM 861, 93–120.

Download references

Author information

Additional information

This research is supported by KBN Grant.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Graczyk, P. Cramér theorem on symmetric spaces of noncompact type. J Theor Probab 7, 609–613 (1994). https://doi.org/10.1007/BF02213571

Download citation

Key Words

  • Symmetric spaces
  • Gaussian measures
  • spherical Fourier transform