A note on three conjectures by Gonchar on rational approximation
type: Item
instance of: scholarly article
title: A note on three conjectures by Gonchar on rational approximation
zbMATH Open document ID: 0635.41015
DOI: 10.1016/0021-9045(87)90060-8
published in: Journal of Approximation Theory
publication date: 1987-01-01T00:00:00Z
review text: The results of this paper have been announced in a preprint of the Technical University Berlin (1985). The main one is the proof of a generalization of a conjecture by A. A. Gonchar on the asymptotics of the order of approximation by rational functions of degree n (nth diagonal Padé approximants) [in the paper read v(f-r) instead of v(f,r)]; log- capacity plays a role. Two other theorems partially prove other conjectures, connected with the asymptotic behaviour of the constant of best-rational approximation on sets where the function is analytic (here plane condensor capacity plays an important role).
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 41A21
Mathematics Subject Classification ID: 41A52
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 4034292
zbMATH Keywords: best constants
zbMATH Keywords: asymptotics of the order of approximation by rational functions
zbMATH Keywords: log-capacity
zbMATH Keywords: best-rational approximation
Wikidata QID: Q123331537
author: Herbert Stahl
reviewed by: Marcel G. de Bruin
MaRDI profile type: Publication
full work available at URL: 0021-9045(87)90060-8
OpenAlex ID: W1968337695
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description: scientific article; zbMATH DE number 4034292