On the neutral Hermite product of the distributions x ±n and δ(m)(x)

Abstract

In this paper, we introduce the neutral Hermite product and study products of tempered distributions based on the Hermite expansions. In particular, we consider products of distributions x n and δ(m)(x) by using the neutral Hermite product and the results are identical with the classical theory of Schwartz distributions. Finally, the recurrence relations about the Hermite expansion coefficients of x ±n δ(m)(x) are obtained for the numerical computation.