Full length article: Weighted Sobolev orthogonal polynomials on the unit ball

Authors:
Teresa E. PéRez;Miguel A. PiñAr;Yuan Xu
Affiliations:
-;-;-
Venue:
Journal of Approximation Theory
Year:
2013

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Abstract

For the weight function W"@m(x)=(1-|x|^2)^@m, @m-1, @l0 and b"@m a normalizing constant, a family of mutually orthogonal polynomials on the unit ball with respect to the inner product =b"@m[@!"B"^"df(x)g(x)W"@m(x)dx+@l@!"B"^"d@?f(x)@?@?g(x)W"@m(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.