Asymptotic Behaviour of the Christoffel Functions on the Unit Ball in the Presence of a Mass on the Sphere
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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.
KeywordsMultivariate orthogonal polynomials unit ball Uvarov modification
Mathematics Subject Classification33C50 42C10
The authors thank MINECO of Spain and the European Regional Development Fund (ERDF) through Grant MTM2014-53171-P, and Junta de Andalucía Grant P11-FQM-7276 and research group FQM–384.
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