Skip to main content
SpringerLink
Log in

A note on stationarity of spherical measures

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

In this short note we show that any smooth probability measure on the boundaryB(G) of a semisimple Lie groupG is stationary for some probability measure on a lattice Γ. This generalizes a result of Furstenberg about Poisson boundaries for semisimple Lie groups.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. F. Bonsall,Decompositions of functions as sums of elementary functions, The Quarterly Journal of Mathematics. Oxford Series (2)37 (1986), 129–136.

    Article  MATH  MathSciNet  Google Scholar 

  2. F. F. Bonsall and D. Walsh,Vanishing l 1-sums of the Poisson kernel, and sums with positive coefficients, Proceedings of the Edinburgh Mathematical Society (2)32 (1989), 431–447.

    Article  MATH  MathSciNet  Google Scholar 

  3. C. Connell and R. Muchnik,Harmonicity of quasi-conformal measure and Poisson boundaries, Geometric and Functional Analysis, to appear.

  4. A. Eskin and C. McMullen,Mixing, counting, and equidistribution in Lie groups, Duke Mathematical Journal71 (1993), 181–209.

    Article  MATH  MathSciNet  Google Scholar 

  5. H. Furstenberg,A Poisson formula for semi-simple Lie groups, Annals of Mathematics (2)77 (1963), 335–386.

    Article  MathSciNet  Google Scholar 

  6. H. Furstenberg,Boundaries of Lie groups and discrete subgroups, Actes du Congres International des Mathématiciens (Nice, 1970), Tome2, Gauthier-Villars, Paris, 1971, pp. 301–306.

    Google Scholar 

  7. W. K. Hayman and T. J. Lyons,Bases for positive continuous functions, Journal of the London Mathematical Society (2)42 (1990), 292–308.

    Article  MATH  MathSciNet  Google Scholar 

  8. W. Rudin,Functional Analysis, International Series in Pure and Applied Mathematics, McGraw-Hill, New York, 1991.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Chicago, 5734 S. University St., 60637, Chicago, IL, USA

    Roman Muchnik

Authors
  1. Roman Muchnik
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The author is supported in part by NSF postdoctoral fellowship.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Muchnik, R. A note on stationarity of spherical measures. Isr. J. Math. 152, 271–283 (2006). https://doi.org/10.1007/BF02771987

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02771987

Keywords

Search

Navigation