Differentiationsalgebren mit einem kubischen Element

Abstract

There are shown new possibilities for the multiplication of some distributions, namely, by means of matrix representations we prove the existence of nontrivial associative differential algebras with an element $h$ satisfying the cubic equation $2h^3-3h^2+h=0$, which can be interpreted as Heaviside’s jump function. One of these algebras is extended by adjunction of an integral of $h$.