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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
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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 are given, which have different properties from the known ones for .

References:

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2.: H. Alexander: Polynomial hulls of graphs, Pacific J. Math. 147 (1991), 201 - 212. MR 91k:32013
3.: 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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5.: 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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7.: J. Wermer: On algebras of continuous functions, Proc. Amer. Math. Soc. 4 (1953), 866-869. MR 15:440g


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