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We discuss approximation of extremal functions by polynomials in the weighted Bergman spaces $$A^p_\alpha $$ A α p where $$-1< \alpha < \min (0,p-2)$$ - 1 < α < min ( 0 , p - 2 ) . We obtain bounds on how close the approximation is to the true extremal function in the $$A^p_\alpha $$ A α p and uniform norms. We also prove several results on the relation between the Bergman modulus of continuity of a function and how quickly its best polynomial approximants converge to it.
Computational Methods and Function Theory – Springer Journals
Published: Jan 24, 2018
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