The principal result of this paper is a proof of the Convolution Theorem based on the definition of a convolution operator as presented by E. M. Stein and R. O'Neil. Closely related are earlier ...

Titchmarsh's convolution theorem states that if the functions f, g vanish on (-∞, 0) and if the convolution f * g(t) = 0 on an interval (0, T), then there are two numbers α, β ≥ 0 such that α + β = T, ...