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


Authors: J. E. Brennan and E. R. Militzer
Original publication: Algebra i Analiz, tom 22 (2010), nomer 1.
Journal: St. Petersburg Math. J. 22 (2011), 41-53
MSC (2010): Primary 30E10
Published electronically: November 16, 2010
MathSciNet review: 2641080
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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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Additional Information

J. E. Brennan
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Email: brennan@ms.uky.edu

E. R. Militzer
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Email: militzer@ms.uky.edu

DOI: https://doi.org/10.1090/S1061-0022-2010-01131-2
Keywords: Polynomial and rational approximation, capacity, peak points, point evaluations
Received by editor(s): November 19, 2009
Published electronically: November 16, 2010
Dedicated: To Victor Havin on his 75th birthday
Article copyright: © Copyright 2010 American Mathematical Society