Weighted Sobolev orthogonal polynomials on the unit ball

• Autores: Teresa E. Pérez, Miguel A. Piñar , Yuan Xu
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 171, Nº 1, 2013, págs. 84-104
• Idioma: inglés
• DOI: 10.1016/j.jat.2013.03.004
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• Resumen

  • For the weight function Wì(x) = (1 . |x|2)ì, ì > .1, ë > 0 and bì a normalizing constant, a family of mutually orthogonal polynomials on the unit ball with respect to the inner product . f, g. = bì ..

    Bd f (x)g(x)Wì(x)dx + ë .

    Bd . f (x) · .g(x)Wì(x)dx .

    are constructed in terms of spherical harmonics and a sequence of Sobolev orthogonal polynomials of one variable. The latter ones, hence, the orthogonal polynomials with respect to .·, ·., can be generated through a recursive formula.