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→∞ 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 (-∞, ∞). 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