Gaussian hemigroups on a locally compact group.

A notion of Gaussian hemigroup is introduced and its relationship with the Gauss condition is studied. Moreover, a Lévy-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. [ABSTRACT FROM AUTHOR]