J. E. Brennan, E. R. Militzer, “<nobr>$L^p$</nobr>-bounded point evaluations for polynomials and uniform rational approximation”, Algebra i Analiz, 2010, Volume 22, Issue 1,Pages <nobr>57

This article is cited in 6 papers

Research Papers

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

J. E. Brennan, E. R. Militzer

Department of Mathematics, University of Kentucky, Lexington, KY

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 $\mathbb C$. Peak points for $R(X)$ and bounded point evaluations for $H^p(X,dA)$, $1\leq p<\infty$, play a fundamental role.

Keywords: polynomial and rational approximation, capacity, peak points, point evaluations.

MSC: 30E10

Received: 19.11.2009

Language: English