Input-output properties of certain stable systems

Input-output properties are discussed of linear systems which have an impulse response of the type w(t, τ)1(t-τ) where ||w(t, τ)|| < c1exp [-c2(t-τ)] for some positive constants c1and c2. It is shown that the square-integrable inputs lead to outputs which are bounded, square integrable, and approach zero as t approaches ∞.