# Orthogonal polynomial projection error measured in Sobolev norms in the unit ball

@article{Figueroa2017OrthogonalPP, title={Orthogonal polynomial projection error measured in Sobolev norms in the unit ball}, author={Leonardo E. Figueroa}, journal={J. Approx. Theory}, year={2017}, volume={220}, pages={31-43} }

We study approximation properties of weighted \(L^2\)-orthogonal projectors onto the space of polynomials of degree less than or equal to N on the unit disk where the weight is of the generalized Gegenbauer form \(x \mapsto (1-\left|x\right|^2)^\alpha \). The approximation properties are measured in Sobolev-type norms involving canonical weak derivatives, all measured in the same weighted \(L^2\) norm. Our basic tool consists in the analysis of orthogonal expansions with respect to Zernike… CONTINUE READING

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## Orthogonal polynomial projection error in Dunkl-Sobolev norms in the ball

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