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

arXiv Mathematics eprints
 Pub Date:
 May 2000
 arXiv:
 arXiv:math/0005297
 Bibcode:
 2000math......5297L
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  Combinatorics;
 Mathematics  Logic
 EPrint:
 Latex. To appear in Hiroshima Math. J