$L^p$-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.References
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Bibliographic 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
- Received by editor(s): November 19, 2009
- Published electronically: November 16, 2010
- © Copyright 2010 American Mathematical Society
- Journal: St. Petersburg Math. J. 22 (2011), 41-53
- MSC (2010): Primary 30E10
- DOI: https://doi.org/10.1090/S1061-0022-2010-01131-2
- MathSciNet review: 2641080
Dedicated: To Victor Havin on his 75th birthday