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arXiv · 1811.10389

Balayage of measures and subharmonic functions on a system of rays. II. Balayage of finite genus and regularity of growth on one ray

B. N. Khabibullin·A. B. Shmeleva·Z. F. Abdullina
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Abstract

We expand the classical balayage of measures and subharmonic functions on a system of rays $S$ with a common origin on the complex plane $\mathbb C$. This allows for an arbitrary subharmonic function $v$ of finite order on $\mathbb C$ build $δ$-subharmonic function on $\mathbb C$, harmonic outside $S$ coinciding with $v$ on $S$ outside the polar set, of the same order of growth as $v$. We give applications to the relationship of the growth of an entire function in $S$ with the distribution of its zeros.

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B. N. Khabibullin, A. B. Shmeleva, Z. F. Abdullina. 2018-11-03. Balayage of measures and subharmonic functions on a system of rays. II. Balayage of finite genus and regularity of growth on one ray. https://arxiv.org/abs/1811.10389

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