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Let $G$ be a compact matrix Lie group with Haar measure $\mu$. Then the heat kernel $\rho: G\times (0,\infty) \rightarrow \mathbb{R}$ satisfies (1) $\rho(g_1g_2,t)=\rho(g_2g_1,t)$ for all positive $t$,...

Let $\mu$ be an infinitely divisible probability on a topological group $G$. If $\nu ^{* n} = \mu$ for some $n$, is $\nu$ an infinitely divisible probability too? A sufficient criterion would be to ...