On the commutative neutrix product of distributions

Abstract

Let f, g be distributions in D' and let f(n)=f * delta(n), g(n)=g * delta(eta), where {delta(eta)} is a certain sequence converging to the Dirac delta-function. The neutrix product f square g is said to exist and be equal to h if [GRAPHICS] for all phi in a. Neutrix products of the form ln(p) x(+) square delta((s)) (x) and x(+)(r) ln x(+) square x(-)(-s) are evaluated from which further neutrix products are obtained.