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The harmonic product of $δ(x_{1},..., x_{n})$ and $δ(x_{1})$ and two combinatorial identities

Ya-Qing Li
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Abstract

In the framework of nonstandard analysis, Bang-He Li and the author defined the product of any two distributions on $R^n$ via their harmonic representations. The product of $δ(x_{1},..., x_{n})$ and $δ(x_{1})$ was calculated by Kuribayashi and the author in [LK]. In this paper, the result of [LK] is improved to $$δ(x_{1},..., x_{n})\circ δ(x_{1}) =\dfrac{1}{2πρ} δ(x_{1},..., x_{n}) {mod} {infinitesimals}$$ where $ρ$ is a positive infinitesimal. Moreover two combinatorial identities are obtained as byproducts.

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Ya-Qing Li. 2000-05-31. The harmonic product of $δ(x_{1},..., x_{n})$ and $δ(x_{1})$ and two combinatorial identities. https://arxiv.org/abs/math/0005297

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