Valiron-Titchmarsh' and Related Theorems for Subharmonic Functions in ${\mathbb{R}}^n$ With Masses on a Half-Line

Abstract

The Valiron-Titchmarsh theorem on asymptotic behavior of entire functions with negative zeros is extended to subharmonic functions in ${\mathbb{R}}^n,n\ge 3$. We also show that the existence of the limit $\lim_{\rti} \frac{\log u(r)}{N(r)}$, where $N(r)$ is the averaged counting function of a subharmonic function $u$ with the associated masses on a ray implies the regular asymptotic behavior separately for $u$ and for $N$.

19 pages. New results added