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  • Author or Editor: Herbert Heyer x
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The main aim of the paper is to prove still another version of the Lvy--Khintchine decomposition of conditionally positive definite functions on a general locally compact Abelian group. The exposition is based on the two-cones theorem proved by N. Drumm in 1976. Application of the main result to the Euclidean group shows the novelty of the approach.

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A notion of Gaussian hemigroup is introduced and its relationship with the Gauss condition is studied. Moreover, a Lvy-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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