Denote by (left(P_{t} ight)) and (left(Q_{t} ight)) respectively the semigroups of the Brownian motion and of the

Denote by \(\left(P_{t}\right)\) and \(\left(Q_{t}\right)\) respectively the semigroups of the Brownian motion and of the \(\mathrm{BES}^{3}\). Prove that \(Q_{t} \Lambda=\Lambda P_{t}\) where

\[\Lambda: f \rightarrow \Lambda f(r)=\frac{1}{2 r} \int_{-r}^{+r} d x f(x)\]