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

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- by John T. Anderson, Alexander J. Izzo and John Wermer
- Proc. Amer. Math. Soc.
**132**(2004), 1495-1500 - DOI: https://doi.org/10.1090/S0002-9939-03-07263-0
- Published electronically: November 14, 2003
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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 $\mathbf {C}^n$.## References

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## Bibliographic Information

**John T. Anderson**- Affiliation: Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, Massachusetts 01610-2395
- MR Author ID: 251416
- 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
- MR Author ID: 307587
- 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
- Received by editor(s): January 15, 2003
- Published electronically: November 14, 2003
- Communicated by: Mei-Chi Shaw
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**132**(2004), 1495-1500 - MSC (2000): Primary 32E30; Secondary 46J10
- DOI: https://doi.org/10.1090/S0002-9939-03-07263-0
- MathSciNet review: 2053357