# 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}
}
• Leonardo E. Figueroa
• Published 2017
• Mathematics, Computer Science
• J. Approx. Theory
• 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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