On multiply monotone functions

Abstract

In this paper, the algebra of the differences of two multiply monotone functions on ${\mathbb{R}}_{+}=(0,+\infty )$ is studied. A sufficient condition for the function $f_0(|x{|}_{p,d})$, where $|x{|}_{p,d}=(\sum _{j=1}^d|x_j{|}^p{)}^{\frac{1}{p}}$, $p\in (0,+\infty ]$, to be represented as the Fourier transform is given.

14 pages; the paper is in Russian, with the abstract and keywords in English