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A Complement to the Valiron-Titchmarsh Theorem for Subharmonic Functions

A Complement to the Valiron-Titchmarsh Theorem for Subharmonic Functions

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, n3. 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 limrlogu(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 Rn with Riesz masses on a ray associated Legendre functions on the cut.