\((0,m)\) Pál-type interpolation on the Möbius transform of roots of unity
type: Item
instance of: scholarly article
title: \((0,m)\) Pál-type interpolation on the Möbius transform of roots of unity
zbMATH Open document ID: 1086.41004
author: Marcel G. de Bruin
published in: Journal of Computational and Applied Mathematics
publication date: 2005-04-18T00:00:00Z
review text: Let \(n,m>1\) be integers and let \(\alpha\) be a complex number such that \(\alpha^2,\alpha^m,\alpha^m,\) \(\alpha^{n+m}\not=1\). For \(k=n\) or \(k=n+m\), consider the complex polynomials \(w_k(z)=(z+\alpha)^k-(1+\alpha z)^k\). The main result is: the \((0,m)\)-Pál-type interpolation problem on the zeros of the pair \(\{w_{n+m}(z),w_n(z)\}\) is regular, i.e. there is a unique complex polynomial \(P(z)\) of degree \(2n+m-1\) which take prescribed values at the zeros of \(w_{n+m}\) and prescribed values of the \(m\)th derivative of \(P(z)\) at the zeros of \(w_n\).
reviewed by: Radu Paltanea
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 30E05
zbMATH DE Number: 2157665
zbMATH Keywords: Pál-type interpolation
zbMATH Keywords: Birkhoff interpolation
zbMATH Keywords: Möbius transform
zbMATH Keywords: regularity
MaRDI profile type: Publication
full work available at URL: j.cam.2003.12.050
OpenAlex ID: W2061144777
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DOI: 10.1016/J.CAM.2003.12.050
description: scientific article; zbMATH DE number 2157665