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.
Acknowledgements
The authors are grateful to Professor Chin Cheng Chou who helped them in the theory of distributions. The authors are also grateful to Professor J.-A. Marti and A. Delcroix for introducing the algebra of Colombeau generalized functions during the summer of 2004 in Shanghai. This work is supported by National Science Foundation of China.