IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v10y1997i4d10.1023_a1022666717516.html
   My bibliography  Save this article

Contractive Automorphisms of Locally Compact Groups and the Concentration Function Problem

Author

Listed:
  • Wojciech Jaworski

Abstract

Let G be a noncompact locally compact group. We show that a necessary and sufficient condition in order that G support an adapted probability measure whose concentration functions fail converge to zero is that G be the semidirect product $$N \times _\tau \mathbb{Z}$$ , where τ is an automorphism of N contractive modulo a compact subgroup. Any adapted a probability measure whose concentration functions fail to converge to zero has the form μ=v×δ1 where v is a probability measure on N. If G is unimodular then the concentration functions of an adapted probability measure μ fail to converge to zero if and only if μ is supported on a coset of a compact normal subgroup.

Suggested Citation

  • Wojciech Jaworski, 1997. "Contractive Automorphisms of Locally Compact Groups and the Concentration Function Problem," Journal of Theoretical Probability, Springer, vol. 10(4), pages 967-989, October.
    • Handle: RePEc:spr:jotpro:v:10:y:1997:i:4:d:10.1023_a:1022666717516
    DOI: 10.1023/A:1022666717516
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1022666717516
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1022666717516?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wojciech Jaworski, 2007. "Dissipation of Convolution Powers in a Metric Group," Journal of Theoretical Probability, Springer, vol. 20(3), pages 487-503, September.
    2. T. M. Retzlaff, 2004. "Decay of Concentration Functions for Adapted Probabilities on Discrete Groups," Journal of Theoretical Probability, Springer, vol. 17(4), pages 1031-1040, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jotpro:v:10:y:1997:i:4:d:10.1023_a:1022666717516. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.