𝐿^{𝑝}-bounded point evaluations for polynomials and uniform rational approximation

Brennan, J.; Militzer, E.

doi:10.1090/S1061-0022-2010-01131-2

$L^p$-bounded point evaluations for polynomials and uniform rational approximation
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by J. E. Brennan and E. R. Militzer

St. Petersburg Math. J. 22 (2011), 41-53

DOI: https://doi.org/10.1090/S1061-0022-2010-01131-2

Published electronically: November 16, 2010

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Abstract:

A connection is established between uniform rational approximation and approximation in the mean by polynomials on compact nowhere dense subsets of the complex plane $\mathbb {C}$. Peak points for $R(X)$ and bounded point evaluations for $H^p(X, dA)$, $1\leq p < \infty$, play a fundamental role.

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