Some dichotomy results for central Gaussian convolution semigroups on compact groups |
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| Authors: | A Bendikov L Saloff-Coste |
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| Institution: | (1) Department of Mathematics, Cornell University, Maloff Hall, Ithaca, NY 14853, USA. e-mail: lsc@math.cornell.edu, US |
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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.
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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