Uniqueness of embedding of Gaussian probability measures into a continuous convolution semigroup on simply connected nilpotent Lie groups

Abstract

Let { μ t ( i ) } t ⩾ 0 ( i = 1 , 2 ) be continuous convolution semigroups on a simply connected nilpotent Lie group G. Suppose that μ 1 ( 1 ) = μ 1 ( 2 ) and that { μ t ( 1 ) } t ⩾ 0 is a Gaussian semigroup (in the sense that its generating distribution just consists of a primitive distribution and a second order differential operator). Then μ t ( 1 ) = μ t ( 2 ) for all t ⩾ 0 . To cite this article: D. Neuenschwander, C. R. Acad. Sci. Paris, Ser. I 346 (2008).