Maximal \(K_n\) domain of a family of rational functions
type: Item
instance of: scholarly article
title: Maximal \(K_n\) domain of a family of rational functions
zbMATH Open document ID: 1065.30012
published in: Mathematical Notes
publication date: 2004-12-07T00:00:00Z
review text: Let \(K_n(D)\) denote a class of functions \(F(z)\) analytic and univalent on a domain \(D\) for which the \(n\)th devided difference \([F(z); z_0,z_1,\dots, z_n]\), does not vanish, provided \(z_k\neq z_l\), \(k\neq l\), \(k,l= 0,1,\dots, n\). The authors are concerned with a family of functions of the form \[ F(z)= \sum^p_{k=1}\,\sum^{m_k}_{s=1} A_{k,s}(z- a_k)^{-s}, \] where constants \(A_{k,s}\), \(a_k\) satisfy certain conditions. They determine, among others, the largest disk \(\Delta_R\) centered at the origin on which \(F(z)\in K_n(\Delta_R)\).
reviewed by: Eligiusz Złotkiewicz
Mathematics Subject Classification ID: 30C55
zbMATH DE Number: 2121457
zbMATH Keywords: rational function
zbMATH Keywords: \(n\)th divided difference
zbMATH Keywords: univalent analytic functions
zbMATH Keywords: Chebyshev system of functions
author: J. Kirjackis
author: E. G. Kiryatzkii
MaRDI profile type: Publication
full work available at URL: b:matn.0000036756.30285.d2
OpenAlex ID: W2055931630
DOI: 10.1023/B:MATN.0000036756.30285.D2
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description: scientific article; zbMATH DE number 2121457