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arXiv · 1705.06710

Uniform Approximation of Extremal Functions in Weighted Bergman Spaces

Timothy Ferguson
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Abstract

We discuss approximation of extremal functions by polynomials in the weighted Bergman spaces $A^p_α$ where $-1 < α< 0$ and $-1 < α< p-2$. We obtain bounds on how close the approximation is to the true extremal function in the $A^p_α$ and uniform norms. We also discuss several results on the relation between the Bergman modulus of continuity of a function and how quickly its best polynomial approximants converge to it.

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Timothy Ferguson. 2017-05-18. Uniform Approximation of Extremal Functions in Weighted Bergman Spaces. https://arxiv.org/abs/1705.06710

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