Schwartz functions, Hadamard products, and the Dixmier-Malliavin theorem

Devadatta G. Hegde

In this paper we show that functions of the form ${\prod }_{n\ge 1}\frac{1}{\left(1+\frac{x^2}{a_n^2}\right)}$ where $a_n>0$ and ${\sum }_{n\ge 1}\frac{1}{a_n^2}<\infty$ are in…