Mean-square approximation by polynomials on the unit disk

Abstract

We investigate P 2 ( μ ) {P^2}(\mu ) , the closure in L 2 ( μ ) {L^2}(\mu ) of the complex polynomials, for certain measures μ \mu on the closed unit disk in the complex plane. Specifically, we present a condition on μ \mu which guarantees that P 2 ( μ ) {P^2}(\mu ) decomposes into a natural direct sum.