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

M.R. Mostova; M.V. Zabolotskyj

doi:10.15330/cmp.7.2.209-214

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

Authors

M.R. Mostova Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine
M.V. Zabolotskyj Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine

https://doi.org/10.15330/cmp.7.2.209-214

Keywords:

logarithmic derivative, entire function, angular density, Fourier coefficients, slowly increasing function

Published online: 2015-12-15

Abstract

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.

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Mostova, M.; Zabolotskyj, M. Convergence in

L^{p} [0, 2 π]

$L^p[0,2\pi]$ -Metric of Logarithmic Derivative and Angular

υ

$\upsilon$ -Density for Zeros of Entire Function of Slowly Growth. Carpathian Math. Publ. 2015, 7, 209-214.

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

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

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