Technical Report CS0080

Title: An Associative, Commutative Distribution Multiplication
Authors: Elemer E. Rosinger
Abstract: An associative and commutative multiplication is defined for the distributions in D'(Rn), by embedding that distribution space in associative and commutative algebras with unit element. The algebras, whose elements are classes of weakly convergent sequences of complex valued smooth functions, were first considered in [12] and [13]. The basic Idea of the distribution multiplication consists in a special representation of the Dirac delta distribution, as a class of weakly convergent sequences of smooth functions satisfying a condition of "strong local presence". The associative and commutative distribution multiplication resulting, proves to be in a sense the best possible within weaker conditions than those given by L. Schwartz in [17], which made impossible any associative multiplication with unit element. Applications to one and three dimensional quantum particle motions in potentials positive powers of the Dirac distribution are presented.
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