Blaschke products and optimal recovery in \(H^{\infty}\)
type: Item
instance of: scholarly article
title: Blaschke products and optimal recovery in \(H^{\infty}\)
zbMATH Open document ID: 0641.30033
DOI: 10.1007/BF02576413
author: T. J. Rivlin
author: Nira Dyn
author: Charles A. Micchelli
published in: Calcolo
publication date: 1987-01-01T00:00:00Z
review text: The error in the optimal estimation of \(\int^{1}_{-1}f(t)w(t)dt\) by a quadrature formula using values of f at equally spaced points of (-1,1) or at the zeros of ultraspherical polynomials is studied. Here f is a holomorphic function on the unit disk which is bounded by 1 and w is a weight function with prescribed behaviour near \(\pm 1\). The study is based on a detailed investigation of bounds on (-1,1) for the finite Blaschke product formed by the nodes of the quadrature formula. Optimal estimation of the function f, rather than its integral, is also investigated.
reviewed by: Jacob Burbea
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 30E05
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 4044176
zbMATH Keywords: optimal recovery
zbMATH Keywords: optimal estimation
zbMATH Keywords: quadrature formula
zbMATH Keywords: Blaschke product
MaRDI profile type: Publication
cites work: On Positive Harmonic Functions and Ultraspherical Polynomials†
cites work: Is Gauss quadrature optimal for analytic functions?
cites work: Optimal interpolation of analytic functions
full work available at URL: https://doi.org/10.1007/bf02576413
OpenAlex ID: W2024318872
description: scientific article; zbMATH DE number 4044176