Products of Distributions: Nonstandard Methods

Abstract

Nonstandard tools are developed which are suitable for studying products of distributions defined by regularization and passage to the limit. We obtain nonstandard criteria for the existence of the products (which are demonstrated to be useful for calculating standard examples) as well as new standard results clarifying the relationship between different types of such products. As an offspring we are able to construct algebras of distributions – as quotients of external spaces of smooth functions – which have properties similar to the Colombeau algebras.

A correction to this paper is available.