Year: 2014
Analysis in Theory and Applications, Vol. 30 (2014), Iss. 1 : pp. 136–140
Abstract
The Valiron-Titchmarsh theorem on asymptotic behavior of entire functions with negative zeros has been recently generalized onto subharmonic functions with the Riesz measure on a half-line in $\mathbb{R}^n$, $n\geq 3$. Here we extend the Drasin complement to the Valiron-Titchmarsh theorem and show that if $u$ is a subharmonic function of this class and of order $0<\rho<1$, then the existence of the limit $\lim_{r \to \infty} \log u(r)/N(r),$ where $N(r)$ is the integrated counting function of the masses of $u$, implies the regular asymptotic behavior for both $u$ and its associated measure.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2014.v30.n1.10
Analysis in Theory and Applications, Vol. 30 (2014), Iss. 1 : pp. 136–140
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 5
Keywords: Valiron-Titchmarsh theorem Tauberian theorems for entire functions with negative zeros Subharmonic functions in $\mathbb{R}^n$ with Riesz masses on a ray associated Legendre functions on the cut.