On polynomials with a prescribed zero on a quasicircle
type: Item
instance of: scholarly article
title: On polynomials with a prescribed zero on a quasicircle
zbMATH Open document ID: 1158.30004
DOI: 10.1007/BF03321686
author: V. V. Andrievskii
author: Stephan Ruscheweyh
published in: Computational Methods and Function Theory
publication date: 2008-07-29T00:00:00Z
review text: Let \(G\) be a finite domain in the complex plane. Fix a point \(z_0\in G\) and a point \(z_1\) on the boundary \(\partial G\). Set \(\alpha_n(G,z_0,z_1):=1-\sup|P_n(z_0)|\), where the supremum is taken over the set of all polynomials of degree \(\leq n\) which vanish at \(z_1\). When \(G={\mathbf D}\) is the unit circle, one has \(c_1n^{-1}\leq \alpha_n(\mathbf{D},z_0,z_1)\leq c_2n^{-1}\), where \(c_1\) and \(c_2\) are absolute constants (this inequality is due to Halász). The authors prove an asymptotically sharp result which extends the result above to quasicircles.
reviewed by: Alexander Ulanovskii
Mathematics Subject Classification ID: 30C10
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 5305536
zbMATH Keywords: polynomial
zbMATH Keywords: zeros
zbMATH Keywords: quasiconformal curve
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5305536