An analogue of Bochner's theorem for Damek-Ricci spaces

Abstract

We characterize the image of radial positive measures $\theta$'s on a harmonic $NA$ group $S$ which satisfies ${\int }_S{\varphi }_0(x)d\theta (x)<\infty$ under the spherical transform, where ${\varphi }_0$ is the elementary spherical function.

arXiv comment11 pages; Comments on the paper are welcome