A survey of representations for multidimensional linear systems: the extra term

A central role in the theory of discrete-time linear systems is played by the idea that every such system has an input-output map that can be represented by a convolution or the familiar generalization of a convolution. This thinking involves an oversight that was previously corrected by adding an additional term to the representation. A need for an additional term arises also in connection with representations for continuous-time linear systems. We survey these results and, in particular, discuss a corresponding result for the important case of representations of multidimensional continuous-space system maps.