On the size of multivariante polynomial lemniscates and the convergence of rational approximants
type: Item
instance of: scholarly article
title: On the size of multivariante polynomial lemniscates and the convergence of rational approximants
zbMATH Open document ID: 1113.41024
author: Zebenzuí García
published in: Journal of Approximation Theory
publication date: 2007-01-26T00:00:00Z
review text: In this paper, nice estimations of the size of the polynomial lemniscate are obtained by the author. Extensions of convergence results for pseudo-rows and Nutall Pommerenke type theorem for a broad class of sequences are obtained by using these estimations. In order to illustrate the convergence results some numerical examples are displayed.
reviewed by: Bhavana Deshpande
Mathematics Subject Classification ID: 41A21
zbMATH DE Number: 5118801
zbMATH Keywords: multivariate Padé approximants
zbMATH Keywords: convergence
zbMATH Keywords: meromorphic functions in several variables
zbMATH Keywords: capacity
zbMATH Keywords: Hausdorff content
MaRDI profile type: Publication
full work available at URL: j.jat.2006.04.003
OpenAlex ID: W2093748764
cites work: Comparison of two capacities in \({\mathbb{C}}^ n\)
cites work: Q3921474
cites work: A new capacity for plurisubharmonic functions
cites work: Polya's inequalities, global uniform integrability and the size of plurisubharmonic lemniscates
cites work: Q3993490
cites work: A multivariate convergence theorem of the ``de Montessus de Ballore'' type
cites work: How well can the concept of Padé approximant be generalized to the multivariate case?
cites work: A direct approach to convergence of multivariate, nonhomogeneous, Padé approximants
cites work: On the size of lemniscates of polynomials in one and several variables
cites work: General order Newton-Padé approximants for multivariate functions
cites work: On rational interpolation to meromophic functions in several variables
cites work: On the convergence of certain sequences of rational approximants to meromorphic functions in several variables
cites work: ON THE CONVERGENCE OF GENERALIZED PADÉ APPROXIMANTS OF MEROMORPHIC FUNCTIONS
cites work: Multivariate Padé approximation.
cites work: Q4693180
cites work: Holomorphic functions of several variables. An introduction to the fundamental theory. With the assist. of Gottfried Barthel transl. by Michael Bridgland
cites work: Q5666837
cites work: The convergence of Padé approximants of meromorphic functions
cites work: Padé approximants and convergence in capacity
cites work: Q3701749
cites work: ON THE CONVERGENCE OF THE PADÉ APPROXIMANTS OF MEROMORPHIC FUNCTIONS
cites work: Volume and capacity of sublevel sets of a Lelong class of plurisubharmonic functions
cites work: The size of plurisubharmonic lemniscates in terms of Hausdorff–Riesz measures and capacities
DOI: 10.1016/J.JAT.2006.04.003
description: scientific article; zbMATH DE number 5118801