## Uniqueness of embedding into a Gaussian semigroup on a nilpotent Lie group.(English)Zbl 0804.60007

It is shown that a Gaussian probability measure has a unique Gaussian embedding convolution semigroup on a simply connected nilpotent Lie group. In other words, if $$(\mu_ t)_{t\geq 0}$$ and $$(\nu_ t)_{t\geq 0}$$ are Gaussian semigroups with $$\mu_ 1= \nu_ 1$$, then $$\mu_ t= \nu_ t$$ for all $$t\geq 0$$.
Reviewer: G.Pap (Debrecen)

### MSC:

 60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
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### References:

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