Asymptotic Behaviour of the Christoffel Functions on the Unit Ball in the Presence of a Mass on the Sphere

Abstract

We present a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes a mass uniformly distributed on the sphere. First, connection formulas relating these multivariate orthogonal polynomials and the classical ball polynomials are obtained. Then, using the representation formula for these polynomials in terms of spherical harmonics analytic properties will be deduced. Finally, we analyse the asymptotic behaviour of the Christoffel functions.