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

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.

Keywords


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

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