Optimal approximants and orthogonal polynomials in several variables II: families of polynomials in the unit ball

Abstract

We obtain closed expressions for weighted orthogonal polynomials and optimal approximants associated with the function) and a scale of Hilbert function spaces in the unit 2-ball having reproducing kernel (1 − z, w ) −γ , γ > 0. Our arguments are elementary but do not rely on reduction to the one-dimensional case.