Convergence in $L^p[0,2\pi]$-metric of logarithmic derivative and angular $\upsilon$-density for zeros of entire function of slowly growth

Convergence in $L^p[0,2\pi]$-metric of logarithmic derivative and angular $\upsilon$-density for zeros of entire function of slowly growth

The subclass of a zero order entire function $f$ is pointed out for which the existence of angular $\upsilon$-density for zeros of entire function of zero order is equivalent to convergence in $L^p[0,2\pi]$-metric of its  logarithmic derivative.

Bibliographic Details
Main Authors: M.R. Mostova, M.V. Zabolotskyj
Format: Article
Language:English
Published: Vasyl Stefanyk Precarpathian National University 2015-12-01
Series:Karpatsʹkì Matematičnì Publìkacìï
Subjects:
logarithmic derivative
entire function
angular density
fourier coefficients
slowly increasing function
Online Access:https://journals.pnu.edu.ua/index.php/cmp/article/view/1399
Description
Summary:The subclass of a zero order entire function $f$ is pointed out for which the existence of angular $\upsilon$-density for zeros of entire function of zero order is equivalent to convergence in $L^p[0,2\pi]$-metric of its  logarithmic derivative.
ISSN:2075-9827
2313-0210

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