Multivariate Sobolev-type orthogonal polynomials

• Mirela V. Mello ^[3] ; Vanessa G. Paschoa ^[1] ; Teresa E. Pérez ^[2] ; Miguel A. Piñar ^[2]
  1. [1] Universidade Estadual de Campinas

     Universidade Estadual de Campinas

     Brasil

     
  2. [2] Universidad de Granada

     Universidad de Granada

     Granada, España

     
  3. [3] Universidade Estadual Paulista, Brazil.

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• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 3, Nº. 2, 2011, págs. 241-259
• Idioma: inglés
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• Resumen

  • Multivariate orthogonal polynomials associated with a Sobolev-type inner product, that is, an inner product defined by adding to a measure the evaluation of the gradients in a fixed point, are studied. Orthogonal polynomials and kernel functions associated with this new inner product can be explicitly expressed in terms of those corresponding with the original measure. We apply our results to the particular case of the classical orthogonal polynomials on the unit ball, and we obtain the asymptotics of the kernel functions.