General Appell systems

Abstract

Given two measures on R^N, p₁, p₂, the convolution p₁ * p₂ is defined by the relation

$$\int {f(x)(p_1 * p_2 )(dx) = \iint {f(x + x\prime)p_1 (dx)p_2 (dx\prime)}}$$

for all bounded continuous functions f. In fact it is sufficient that this relation hold for all complex exponentials e^iax, with a ∈ R^N.