A reverse cos\(\pi \rho \) theorem and a question of Fryntov
type: Item
instance of: scholarly article
title: A reverse cos\(\pi \rho \) theorem and a question of Fryntov
zbMATH Open document ID: 1247.30045
DOI: 10.1007/BF03321820
author: P. C. Fenton
author: John Rossi
published in: Computational Methods and Function Theory
publication date: 2012-06-25T00:00:00Z
review text: The authors prove the following theorem. Suppose that \(u\) is subharmonic in the plane and that \(G\) is an open set in which \(m \{ \theta: r e^{i \theta} \in G \} \geq 2 (\pi - \alpha)\) for all large \(r\) and for some number \(\alpha\) satisfying \(0 < \alpha < \pi\). Given any \(\lambda \) satisfying \(0 < \alpha \lambda \leq \pi/2\), either \(A(r, u) > \cos (\alpha \lambda) B(r, u)\) for certain arbitrary large values of \(r\) or \(\lim_{r \to \infty} \frac{B(r, u)}{r^\lambda}\) exists and is either positive or \(+ \infty\). Here \(A(r, u) =\inf_\theta u(r e^{i \theta}), B(r, u) = \sup_\theta u(r e^{i \theta})\). The authors further discuss a connection between this theorem and conjectures of A. Eremenko, A. Fryntov and T. Kövari.
Mathematics Subject Classification ID: 30D15
zbMATH DE Number: 6049590
zbMATH Keywords: subharmonic function
zbMATH Keywords: entire function
zbMATH Keywords: \(\cos \pi \rho \) theorem
zbMATH Keywords: gap series
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03321820
OpenAlex ID: W1981379755
description: scientific article; zbMATH DE number 6049590