Discrete Time Scattering and Wold’s Decomposition in Pictures

Based on explicit computations, various concepts of discrete time scattering theory are reviewed, discussed, and illustrated. The dynamics take place on a discrete half-space. All operators are represented graphically. The expressions obtained for the wave operators lead to an easily visualized interpretation of Wold’s decomposition, a seminal result of operator theory. This work has a clear pedagogical orientation, with the aim of providing explicit formulas and graphical representations for operators which are usually only known to exist.