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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
MathSciNet review:
1610917
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Abstract:
Let be the graph of a continuous map of the unit sphere of into , and the polynomially convex hull of . Several examples of for are given, which have different properties from the known ones for .
References:
- 1.
- P. Ahern and W.Rudin: Hulls of 3-spheres in
, Contemporary Math. 137 (1992), 1 - 27. MR 93k:32020 - 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
- 4.
- H. Alexander and J. Wermer: Polynomial hulls with convex fibers, Math. Ann. 271 (1985), 99-109. MR 86i:32025
- 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
- 6.
- A. Sakai: Uniform approximation in several complex variables, Osaka J. Math. 15 (1978), 586 - 611. MR 81e:32019
- 7.
- 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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