Polynomial approximation on three-dimensional real-analytic submanifolds of $\mathbf {C}^n$
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- by John T. Anderson, Alexander J. Izzo and John Wermer
- Proc. Amer. Math. Soc. 129 (2001), 2395-2402
- DOI: https://doi.org/10.1090/S0002-9939-01-05911-1
- Published electronically: January 18, 2001
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Abstract:
It was once conjectured that if $A$ is a uniform algebra on its maximal ideal space $X$ and if each point of $X$ is a peak point for $A$, then $A = C(X)$. This peak point conjecture was disproved by Brian Cole in 1968. However, it was recently shown by Anderson and Izzo that the peak point conjecture does hold for uniform algebras generated by smooth functions on smooth two-manifolds with boundary. Although the corresponding assertion for smooth three-manifolds is false, we establish a peak point theorem for real-analytic three-manifolds with boundary.References
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Bibliographic Information
- John T. Anderson
- Affiliation: Department of Mathematics, College of the Holy Cross, Worcester, Massachusetts 01610
- MR Author ID: 251416
- Email: anderson@math.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, Texas A & M University, College Station, Texas 77843
- MR Author ID: 307587
- Email: aizzo@math.bgsu.edu, aizzo@math.tamu.edu
- John Wermer
- Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912
- Email: wermer@math.brown.edu
- Received by editor(s): December 28, 1999
- Published electronically: January 18, 2001
- Communicated by: Steven R. Bell
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2395-2402
- MSC (2000): Primary 32E30; Secondary 46J10
- DOI: https://doi.org/10.1090/S0002-9939-01-05911-1
- MathSciNet review: 1823924