On the non-commutative neutrix product of Dirac-delta distribution with an infinitely differentiable function

Abstract

In this article, we first consider the non-commutative neutrix product of f +(x) and δ(r)(x) and also the product of f −(x) and δ(r)(x) for r=0, 1, 2, …, where f is an infinitely differentiable function and f +(x)=H(x)f(x) and f −(x)=H(−x)f(x), H denoting Heaviside’s function. Then we generalize some results obtained by Fisher [Fisher, B., 1971, The product of distributions. Quarterly Journal of Mathematics Oxford, 22, 291–298 and Fisher, B., 1982, A non-commutative neutrix product of distributions. Mathematische Nachrichten, 108, 117–127.].