Mathematics > Complex Variables
[Submitted on 4 Dec 2018 (v1), last revised 10 Feb 2020 (this version, v2)]
Title:On the Heins Theorem
View PDFAbstract:It is known that the famous Heins Theorem (also known as the de Branges Lemma) about the minimum of two entire functions of minimal type does not extend to functions of finite exponential type. We study in detail pairs of entire functions $f, g$ of finite exponential type satisfying $\sup_{z\in\mathbb{C}}\min\{|f(z)|,|g(z)|\}<\infty.$ It turns out that $f$ and $g$ have to be bounded on some rotating half-planes. We also obtain very close upper and lower bounds for possible rotation functions of these half-planes.
Submission history
From: Aleksei Kulikov [view email][v1] Tue, 4 Dec 2018 22:28:51 UTC (11 KB)
[v2] Mon, 10 Feb 2020 11:34:13 UTC (12 KB)
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