On functions that satisfy a weakened asymptotic monogeny condition
type: Item
instance of: scholarly article
title: On functions that satisfy a weakened asymptotic monogeny condition
zbMATH Open document ID: 0951.30003
DOI: 10.1007/BF02908439
published in: Analysis Mathematica
publication date: 2000-11-13T00:00:00Z
review text: Given a complex function \(f\) in a domain \(D\), the following theorem is proved: if there exists a positive number \(\sigma\), such that \(f\) is monogenic at any \(\xi\in D\) relatively some set \(G(\xi)\) with the lower density at \(\xi\) greater than \(\sigma+\frac{1}{2}\) then one can find \(p_{\sigma\geq 1}\) such that local summability of the function \((\log^+|f(z)|)^{p_{\sigma}}\) implies that \(f\) is holomorphic in \(D\), with the asymptotic estimate \(p_{\sigma}=O(|\log\sigma|\sigma^{-\frac{3}{2}})\) for \(\sigma\to +0\) and for \(\sigma\geq\frac{11}{24}\) one can take \(p_{\sigma}:=1\). This paper continues the author's research on relations between asymptotic monogeneity and analyticity of complex functions.
Mathematics Subject Classification ID: 30A05
zbMATH DE Number: 1528693
zbMATH Keywords: holomorphic functions
zbMATH Keywords: asymptotic monogeneity
author: D. S. Telyakovskij
reviewed by: M. Shapiro
MaRDI profile type: Publication
cites work: Q3362668
description: scientific article; zbMATH DE number 1528693