  For smooth bounded open sets in euclidean space, we construct corresponding
contractive linear extension operators for the space of continuous functions
which preserve regularity of functions in the domain of the Robin Laplacian. We
also prove a Trotter-like approximation for the semigroup generated by the
Laplacian subject to Robin boundary conditions in terms of these extension
operators. The limiting case of Dirichlet boundary conditions is treated
separately.
