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

  • Clotilde Martínez
  • Miguel A. PiñarEmail author


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.


Multivariate orthogonal polynomials unit ball Uvarov modification 

Mathematics Subject Classification

33C50 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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Departamento de Matemática AplicadaUniversidad de GranadaGranadaSpain

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