Markov processes are well understood in the case when they take place in the whole Euclidean space. The situation becomes much more complicated if a Markov process is restricted to a domain with boundary, and a satisfactory theory exists only for processes with continuous trajectories. The aim of the talk is to present joint results with Tony Hill on a model Wiener-Hopf plus Mellin operator, which is related to the generator of a symmetric stable  Levy process on a half-line.