A New Theory for Fourier Analysis. V. Generalized Multiplication and Convolution on the Dual Space

Definitions for the multiplication and convolution of fairly arbitrary pairs of elements in the dual to the space of "exponentially decreasing" analytic test functions are presented. These definitions greatly extend previous definitions and are shown to be consistent with suitably defined products and convolutions on other topological vector spaces. Basic properties of multiplication and convolution are demonstrated and simple examples are given