A compact set with noncompact disc-hull
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- by Buma Fridman, Lop-Hing Ho and Daowei Ma PDF
- Proc. Amer. Math. Soc. 129 (2001), 1473-1475 Request permission
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
- Patrick Ahern and Walter Rudin, Hulls of $3$-spheres in $\textbf {C}^3$, The Madison Symposium on Complex Analysis (Madison, WI, 1991) Contemp. Math., vol. 137, Amer. Math. Soc., Providence, RI, 1992, pp. 1–27. MR 1190966, DOI 10.1090/conm/137/1190966
- Walter Rudin, Real and complex analysis, 2nd ed., McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1974. MR 0344043
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
- Received by editor(s): August 31, 1999
- Published electronically: October 25, 2000
- Communicated by: Steven R. Bell
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1473-1475
- MSC (2000): Primary 32E20
- DOI: https://doi.org/10.1090/S0002-9939-00-05704-X
- MathSciNet review: 1814175