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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Polynomially convex hulls of graphs on the sphere

Author(s): Toshiya Jimbo; Akira Sakai
Journal: Proc. Amer. Math. Soc. 127 (1999), 2697-2702.
MSC (1991): Primary 32E20
Posted: April 15, 1999
MathSciNet review: 1610917
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Abstract | References | Similar articles | Additional information

Abstract: Let $\Sigma$ be the graph of a continuous map of the unit sphere of $\mathbb C^n$ into $\mathbb C^m$, and $h(\Sigma)$ the polynomially convex hull of $\Sigma$. Several examples of $h(\Sigma)$ for $n=m>1$ are given, which have different properties from the known ones for $n>m$.


References:

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P. Ahern and W.Rudin: Hulls of 3-spheres in $\mathbb  C^3$, Contemporary Math. 137 (1992), 1 - 27. MR 93k:32020

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H. Alexander: Polynomial hulls of graphs, Pacific J. Math. 147 (1991), 201 - 212. MR 91k:32013

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J. T. Anderson: On an example of Ahern and Rudin, Proc. Amer. Math. Soc. 116 (1992), 695 - 699. MR 93c:32021

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H. Alexander and J. Wermer: Polynomial hulls with convex fibers, Math. Ann. 271 (1985), 99-109. MR 86i:32025

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S. N. Mergelyan: Uniform approximation to functions of a complex variable, Uspehi Mat. Nauk. 7 (1952), No.2, 31-122; Amer. Math. Soc Transl. 3 (1962), Ser.1, 294-391. MR 14:547e

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A. Sakai: Uniform approximation in several complex variables, Osaka J. Math. 15 (1978), 586 - 611. MR 81e:32019

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J. Wermer: On algebras of continuous functions, Proc. Amer. Math. Soc. 4 (1953), 866-869. MR 15:440g


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Additional Information:

Toshiya Jimbo
Affiliation: Department of Mathematics, Nara University of Education, Takabatake, Nara 630-8528, Japan
Email: jimbo@nara-edu.ac.jp

Akira Sakai
Affiliation: Yamadanishi 2-9,A3-612 Suita, Osaka 565-0824, Japan
Email: CXH02215@niftyserve.or.jp

DOI: 10.1090/S0002-9939-99-04922-9
PII: S 0002-9939(99)04922-9
Received by editor(s): November 20, 1997
Posted: April 15, 1999
Communicated by: Theodore W. Gamelin
Copyright of article: Copyright 1999, American Mathematical Society




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