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Some dichotomy results for central Gaussian convolution semigroups on compact groups
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  • Published: December 2002

Some dichotomy results for central Gaussian convolution semigroups on compact groups

  • A. Bendikov1 &
  • L. Saloff-Coste1 

Probability Theory and Related Fields volume 124, pages 561–573 (2002)Cite this article

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  • 3 Citations

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Abstract.

 Consider a central Gaussian convolution semigroup (μ t ) t > 0 on a connected compact semisimple group. Then either the measure μ t is singular with respect to Haar measure for all t > 0, or there exists a time t such that μ t is absolutely continuous with respect to Haar measure and admits a continuous density.

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Authors and Affiliations

  1. Department of Mathematics, Cornell University, Maloff Hall, Ithaca, NY 14853, USA. e-mail: lsc@math.cornell.edu, , , , , , US

    A. Bendikov & L. Saloff-Coste

Authors
  1. A. Bendikov
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  2. L. Saloff-Coste
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Additional information

Received: 6 November 2001 / Revised version: 13 June 2002 / Published online: 30 September 2002

Research partially supported by NSF grant DMS 0102126

Mathematics Subject Classification (2000): 28C10, 28C20, 60B15, 60G30

Keywords or phrases: Gaussian convolution semigroups – Dichotomy – Absolute continuity

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Bendikov, A., Saloff-Coste, L. Some dichotomy results for central Gaussian convolution semigroups on compact groups. Probab Theory Relat Fields 124, 561–573 (2002). https://doi.org/10.1007/s00440-002-0228-0

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  • Issue Date: December 2002

  • DOI: https://doi.org/10.1007/s00440-002-0228-0

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Keywords

  • Convolution
  • Compact Group
  • Dichotomy Result
  • Continuous Density
  • Semisimple Group
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