SOME RESULTS ON THE COMMUTATIVE NEUTRIX PRODUCT OF DISTRIBUTIONS

Abstract. Let f, g be distributions in D ′ and let fn = f ∗ δn, gn = g ∗ δn, where {δn} is a certain sequence converging to the Dirac delta-function. The neutrix product fg is said to exist and be equal to h if N−lim n→∞ 〈fngn, φ 〉 = 〈h, φ〉 for all φ in D. Neutrix products of the form lnx+δ (s)(x) and x−s+ δ (s)(x) are evaluated from which further neutrix products are obtained. The following definition of a neutrix was given by van der Corput [1]: Difinition 1. Let N be an additive group of functions defined on a set N ′ with values in an additive group N ′ ′ with the property that the only constant function in N is the zero function. Then N is said to be a neutrix and the functions in N are said to be negligible