3 problems

Generalized path-sum conjecture. This formula should define the Ornstein–Uhlenbeck semigroup on an arbitrary graph, for all $t>0$ and $x\in{\mathcal G}$.

Let $R_+$ be the set of positive roots, let $\gamma$ be the parameter appearing in the generalized Ornstein–Uhlenbeck semigroup, and let $T$ and $\Gamma_k$ be the operators in Theo…

Let $(\mathcal H_t)_{t>0}$ be the Ornstein–Uhlenbeck transition semigroup on $\mathbb R^n$ with invariant measure $\gamma_\infty$. For $f\in L^1(\gamma_\infty)$, write…