Lp-bounded point evaluations for polynomials and uniform rational approximation

J. E. Brennan; E. R. Militzer

doi:10.1090/S1061-0022-2010-01131-2

L^p-bounded point evaluations for polynomials and uniform rational approximation

J. E. Brennan, E. R. Militzer

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

A connection is established between uniform rational approximation and approximation in the mean by polynomials on compact nowhere dense subsets of the complex plane ℂ. Peak points for R(X) and bounded point evaluations for H^p(X, dA), 1 ≤ p < ∞, play a fundamental role.

Original language	English
Pages (from-to)	41-53
Number of pages	13
Journal	St. Petersburg Mathematical Journal
Volume	22
Issue number	1
DOIs	https://doi.org/10.1090/S1061-0022-2010-01131-2
State	Published - 2011

Keywords

Capacity
Peak points
Point evaluations
Polynomial and rational approximation

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Applied Mathematics

Access to Document

10.1090/S1061-0022-2010-01131-2

Cite this

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title = "Lp-bounded point evaluations for polynomials and uniform rational approximation",

abstract = "A connection is established between uniform rational approximation and approximation in the mean by polynomials on compact nowhere dense subsets of the complex plane ℂ. Peak points for R(X) and bounded point evaluations for Hp(X, dA), 1 ≤ p < ∞, play a fundamental role.",

keywords = "Capacity, Peak points, Point evaluations, Polynomial and rational approximation",

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