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Absolute continuity, singularity, and supports of Gauss semigroups on a Lie group

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Abstract

A Gauss semigroupS on a connected Lie group is absolutely continuous if and only if a certain differential operator associated withS is hypoelliptic. OtherwiseS is singular. IfS is absolutely continuous it has remarkable differentiability properties. Moreover the supports of the measures inS are described. The general results are specialized to the group of affine mappings on the real line.

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  1. Mathematisches Institut der Universität, Auf der Morgenstelle 10, D-7400, Tübingen, Federal Republic of Germany

    Eberhard Siebert

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  1. Eberhard Siebert
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Siebert, E. Absolute continuity, singularity, and supports of Gauss semigroups on a Lie group. Monatshefte für Mathematik 93, 239–253 (1982). https://doi.org/10.1007/BF01299300

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  • DOI: https://doi.org/10.1007/BF01299300

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