Uniqueness of Embedding into a Gaussian Semigroup and a Poisson Semigroup with Determinate Jump Law on a Simply Connected Nilpotent Lie Group

摘要

Let {μ t (i) } t≥0 (i=1,2) be continuous convolution semigroups (c.c.s.) on a simply connected nilpotent Lie group G. Suppose that μ 1 (1) =μ 1 (2) . Assume furthermore that one of the following two conditions holds: The c.c.s. {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)