Website owner:  James Miller

Prove:

Proof. We will give a line of reasoning confirming 1). Property 2) follows directly from 1) since δ(0) occurs at G(a). Let us view the Dirac delta function as the limit of the function F_ε(t)

as ε as shown in Fig. 1. Because the product F_ε(t)G(t) is equal to zero outside the interval [0, t] we have

See Fig. 2. Now it is fairly obvious that, considering the limit as t ,

where is the average value of the function y = G(t) within the interval Δt and Δt = ε. See Fig. 3. In addition, as t , . Thus we arrive at

Website owner:  James Miller