Gaussian hemigroups on a locally compact group

Heyer, Herbert and Pap, Gyula (2004) Gaussian hemigroups on a locally compact group. Acta Mathematica Hungarica, 103 (3). pp. 197-224. ISSN 0236-5294 (print), 1588-2632 (online)

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Abstract

A notion of Gaussian hemigroup is introduced and its relationship with the Gauss condition is studied. Moreover, a Levy-type martingale characterization is proved for processes with independent (not necessarily stationary) increments satisfying the Gauss condition in a compact Lie group. The characterization is given in terms of a faithful finite dimensional representation of the group and its tensor square. For the proofs noncommutative Fourier theory is applied for the convolution hemigroups associated with the increment processes.

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