Resumen de Weighted Sobolev orthogonal polynomials on the unit ball

Teresa E. Pérez, Miguel A. Piñar, Yuan Xu

• 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.