Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Un théorème de Choquet-Deny pour les groupes moyennables
Download PDF
Download PDF
  • Published: December 1988

Un théorème de Choquet-Deny pour les groupes moyennables

  • Albert Raugi1 

Probability Theory and Related Fields volume 77, pages 481–496 (1988)Cite this article

  • 84 Accesses

  • 3 Citations

  • Metrics details

Summary

LetG be a connected locally compact separable amenable group. Let σ be a positive measure on the Borel σ-field ofG. We study the positive Borel functionsh onG which satisfy: ∀g ∑G,\(\int\limits_G {h(g x) \sigma (d x)} = \int\limits_G {h(x g) \sigma } (d x) = h(g)\). Under “smooth” assumptions on σ, we establish an integral representation of these functions in term of exponentials.

Résumé

SoitG un groupe moyennable connexe, locallement compact, à base dénombrable. Soit σ une mesure positive sur les boréliens deG. Nous étudions les fonctions boréliennes positivesh vérifiant: ∀g ∑G,\(\int\limits_G {h(g x) \sigma (d x)} = \int\limits_G {h(x g) \sigma } (d x) = h(g)\). Sous “de bonnes” hypothèses sur σ, nous obtenons, pour ces fonctions, une représentation intégrale à l'aide d'exponentielles.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Choquet, G., Deny, J.: Sur l'équation de convolution μ=μ*σ. C.R.A.S.,250, 799–801 (1960)

    Google Scholar 

  2. Chevalley, C.: Théorie des groupes de Lie. Pub. de l'Inst. de Mathématiques de l'Université de Nancago. Paris: Hermann 1968

    Google Scholar 

  3. Elie, L.: Fonctions harmoniques positives sur le groupe affine. Probability measures on groups. Proceedings Oberwolfach 1978. (Lect. Notes Math., vol. 706, pp. 96–110) Berlin Heidelberg New York: Springer 1979

    Google Scholar 

  4. Guivarc'h, Y.: Théorèmes quotients pour les marches aléatoires. Astérisque74, 15–28 (1980)

    Google Scholar 

  5. Montgomery, D., Zippin, L.: Topological transformation groups. New York: Interscience 1955

    Google Scholar 

  6. Raugi, A.: Fonctions harmoniques et théorèmes limites pour les marches aléatoires sur les groupes. Bull. Soc. Math. Fr. mémoire54, 5–118 (1977)

    Google Scholar 

  7. Raugi, A.: Un théorème de Choquet-Deny pour les semi-groupes abéliens. Théorie du potentiel, proceedings, Orsay 1983. (Lect. Notes Math., vol. 1096, pp. 502–520) Berlin Heidelberg New York: Springer 1984

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IRMAR, U.E.R. de Mathématiques, Université de Rennes I, Campus Beaulieu, F-35042, Rennes Cedex, France

    Albert Raugi

Authors
  1. Albert Raugi
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Raugi, A. Un théorème de Choquet-Deny pour les groupes moyennables. Probab. Th. Rel. Fields 77, 481–496 (1988). https://doi.org/10.1007/BF00959612

Download citation

  • Received: 08 December 1986

  • Revised: 28 November 1987

  • Issue Date: December 1988

  • DOI: https://doi.org/10.1007/BF00959612

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature