Approximately-finite memory and input-output maps

A body of results is given concerning the character of the response of systems represented by approximately-finite-memory input-output maps G. Conditions are given under which, for example, the system's output approaches a limit as t to infinity whenever the input does. Of particular interest are theorems that concern the existence and properties of a certain unique extension of G to a corresponding domain of functions defined on all of (- infinity , infinity ). The theorems lead to some general propositions that characterize the response of nonlinear systems to asymptotically almost periodic inputs. These concern, for example, the spectrum of the system's steady-state output as well as an analytical basis for the computation of this output.>