Products of distributions: Nonstandard methods
Let S and T be distributions on \(R^ n\) and define their product as \(\lim_{\epsilon \to 0}(S*\phi_{\epsilon})(T*\phi_{\epsilon})\) provided the limit exists in \({\mathcal D}'(R^ n)\) for certain classes of delta-nets. Four such classes of delta-nets are considered in the literature leading to four definitions of the product. In this work the author obtains nostandard criteria for the existence of some of these products as well as new standard results concerning the relationship between them.
nostandard criteria for the existence of some of these products
scientific article; zbMATH DE number 4082295