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

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The Valiron-Titchmarsh theorem on asymptotic behavior of entire functions with negative zeros is extended to subharmonic functions in $\mathbb{R}^n, n\geq 3$. We also show that the existence of the limit $\lim { ti} \frac{\log ur}{Nr}$, where $Nr$ 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 $N$.

Author: Alexander I. Kheyfits

Source: https://archive.org/