Physical Sciences and Mathematics Commons^™

LP Bounded Point Evaluations For Polynomials And Uniform Rational Approximation, Erin Militzer

University of Kentucky Doctoral Dissertations

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.