Leonardo E. Figueroa:
Error in Sobolev norms of orthogonal projection onto polynomials in the unit ball
We study approximation properties of weighted L2-orthogonal projectors onto spaces of polynomials of bounded degree in the Euclidean unit ball, where the weight is of a generalized Gegenbauer form. Said properties are measured in Sobolev-type norms in which the same weighted L2 norm is used to control all involved weak derivatives. The method of proof does not rely on any particular basis of orthogonal polynomials, which allows for a streamlined and dimension-independent exposition.
This preprint gave rise to the following definitive publication(s):
Leonardo E. FIGUEROA: Orthogonal polynomial projection error measured in Sobolev norms in the unit ball. Journal of Approximation Theory, vol. 220, pp. 31-43, (2017).