Discrete time scattering and Wold's decomposition in pictures

Abstract

Based on explicit computations, various concepts of discrete time scattering theory are reviewed, discussed, and illustrated. The dynamics are taking 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 is clearly pedagogically oriented with the aim of providing explicit formulas and pictures for usually unexplicit operators.