A representation theorem for linear systems

The cornerstone of the theory of discrete-time single-input single-output linear systems is the idea that every such system has an input-output map H that can be represented by a convolution or the familiar generalization of a convolution. This thinking involves an oversight that was recently corrected by adding an additional term to the representation. Here we give a corresponding result for the important case of representations of causal continuous-time system maps that take bounded functions into bounded functions.