On uniform tangential approximations by lacunary power series on curves in the complex plane
type: Item
instance of: scholarly article
title: On uniform tangential approximations by lacunary power series on curves in the complex plane
zbMATH Open document ID: 0832.32014
author: Yanyan Li
published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences
publication date: 1995-10-18T00:00:00Z
review text: Let \(D_R\) denote the \(\text{disc} \{|z |< R\}\) for \(0 < R \leq \infty\). For an appropriate piecewise smooth Jordan \(\text{arc} \Gamma_0\) in \(D_R\) joining the origin and a point of \(\partial D_R\), put \(E_m = \cup^{m - 1}_{k = 0} \Gamma_k\), where \(\Gamma_k = \{z \in D_R : z = w \exp (2 \pi ik/m)\), \(w \in \Gamma_0\}\). The authors prove: For an appropriate lacunary sequence \(Q\) and for \(\varepsilon > 0\) and \(f\) arbitrary continuous functions on \(E_m\), there exists a function \(g\) holomorphic in \(D_R\), \(g(z) = \sum_{n \in Q} g_n z^n\), such that \(|f(z) - g(z) |< \varepsilon (z)\), \(\forall z \in E_m\).
Mathematics Subject Classification ID: 32E30
Mathematics Subject Classification ID: 32E10
Mathematics Subject Classification ID: 30B10
zbMATH DE Number: 795443
zbMATH Keywords: tangential approximation
zbMATH Keywords: lacunary power series
reviewed by: Edwin J. Akutowicz
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 795443