2017
Том 69
№ 9

All Issues

On the Growth of Infinite-Order Subharmonic Functions in ℂ

Kondratyuk Ya. V.

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Abstract

For infinite-order functions u subharmonic in \(\mathbb{C}\) with given restrictions on the Riesz masses of a disk of radius r ∈ (0, +∞), we find majorants for the functions \(B\left( {r,u} \right) = \max \left\{ {\left| {u\left( z \right)} \right|:\left| z \right| \leqslant r} \right\}\) and \(\overset{\lower0.5em\hbox{\(\smash{\scriptscriptstyle\smile}\)}}{B} \left( {r,u} \right) = \sup \left\{ {\left| {\overset{\lower0.5em\hbox{\(\smash{\scriptscriptstyle\smile}\)}}{u} \left( z \right)} \right|:\left| z \right| \leqslant r} \right\}\) , where \(\overset{\lower0.5em\hbox{\(\smash{\scriptscriptstyle\smile}\)}}{u}\) is a function conjugate to u.

English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 9, pp 1540-1546.

Citation Example: Kondratyuk Ya. V. On the Growth of Infinite-Order Subharmonic Functions in ℂ // Ukr. Mat. Zh. - 2002. - 54, № 9. - pp. 1276-1281.

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