Heat semigroup
= Heat semigroup
{title2=$(P_t)$}
The heat semigroup acts by convolution with the heat kernel: $P_tf=K_t*f$. The identity $K_s*K_t=K_{s+t}$ gives $P_sP_t=P_{s+t}$, and its infinitesimal generator is a constant multiple of the Laplacian.