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A compact set with noncompact disc-hull


Authors: Buma Fridman, Lop-Hing Ho and Daowei Ma
Journal: Proc. Amer. Math. Soc. 129 (2001), 1473-1475
MSC (2000): Primary 32E20
DOI: https://doi.org/10.1090/S0002-9939-00-05704-X
Published electronically: October 25, 2000
MathSciNet review: 1814175
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Abstract:

The disc-hull of a set is the union of the set and all $H^\infty $discs whose boundaries lie in the set. We give an example of a compact set in $\mathbb{C}^2$ whose disc-hull is not compact, answering a question posed by P. Ahern and W. Rudin.


References [Enhancements On Off] (What's this?)

  • 1. Patrick Ahern and Walter Rudin.
    Hulls of 3-spheres in $\mathbb{C}^3$.
    Contemporary Math., v 137, Amer. Math. Soc., Providence, RI, 1992, 1-27. MR 93k:32020
  • 2. Walter Rudin.
    Real and Complex Analysis, 2nd ed.
    McGraw-Hill, New York, 1974. MR 49:8783

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Additional Information

Buma Fridman
Affiliation: Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas 67260-0033
Email: fridman@math.twsu.edu

Lop-Hing Ho
Affiliation: Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas 67260-0033
Email: lho@twsuvm.uc.twsu.edu

Daowei Ma
Affiliation: Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas 67260-0033
Email: dma@math.twsu.edu

DOI: https://doi.org/10.1090/S0002-9939-00-05704-X
Keywords: Polynomial convexity, disc-hull
Received by editor(s): August 31, 1999
Published electronically: October 25, 2000
Communicated by: Steven R. Bell
Article copyright: © Copyright 2000 American Mathematical Society

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