Theorem 12.24 (Convolution Theorem).  Let and denote the Laplace transforms of and , respectively.  Then the product    is the Laplace transform of the convolution of    and ,  and is denoted by  ,  and has the integral representation  

                

Proof.

Proof of Theorem 12.24.

Proof of Theorem 12.24 is in the book.

Complex Analysis for Mathematics and Engineering

(c) 2006 John H. Mathews, Russell W. Howell