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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Polynomial approximation on real-analytic varieties in $\mathbf{C}^n$


Authors: John T. Anderson, Alexander J. Izzo and John Wermer
Journal: Proc. Amer. Math. Soc. 132 (2004), 1495-1500
MSC (2000): Primary 32E30; Secondary 46J10
Published electronically: November 14, 2003
MathSciNet review: 2053357
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Abstract: We prove: Let $\Sigma$ be a compact real-analytic variety in $\mathbf{C}^n$. Assume (i) $\Sigma$ is polynomially convex and (ii) every point of $\Sigma$ is a peak point for $P(\Sigma)$. Then $P(\Sigma) = C(\Sigma)$. This generalizes a previous result of the authors on polynomial approximation on three-dimensional real-analytic submanifolds of $\mathbf{C}^n$.


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Additional Information

John T. Anderson
Affiliation: Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, Massachusetts 01610-2395
Email: anderson@mathcs.holycross.edu

Alexander J. Izzo
Affiliation: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403
Address at time of publication: Department of Mathematics, Brown University, Providence, RI 02912
Email: aizzo@math.bgsu.edu, aizzo@math.brown.edu

John Wermer
Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912
Email: wermer@math.brown.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07263-0
PII: S 0002-9939(03)07263-0
Received by editor(s): January 15, 2003
Published electronically: November 14, 2003
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2003 American Mathematical Society