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 Rn, n≥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<ρ<1, then the existence of the limit lim 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.