Bounded holomorphic functions of several complex variables. I
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- by Dong Sie Kim PDF
- Trans. Amer. Math. Soc. 158 (1971), 437-443 Request permission
Abstract:
A domain of bounded holomorphy in a complex analytic manifold is a maximal domain for which every bounded holomorphic function has a bounded analytic continuation. In this paper, we show that this is a local property: if, for each boundary point of a domain, there exists a bounded holomorphic function which cannot be continued to any neighborhood of the point, then there exists a single bounded holomorphic function which cannot be continued to any neighborhood of the boundary points.References
- Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696
- Lars Hörmander, An introduction to complex analysis in several variables, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0203075 F. Quigley, Lectures on several complex variables, Tulane University, New Orleans, La., 1964/65, 1965/66.
- Walter Rudin, Some theorems on bounded analytic functions, Trans. Amer. Math. Soc. 78 (1955), 333–342. MR 67192, DOI 10.1090/S0002-9947-1955-0067192-5 M. Shauck, Algebras of holomorphic functions in ringed spaces, Dissertation, Tulane University, New Orleans, La., 1966.
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 158 (1971), 437-443
- MSC: Primary 32.20
- DOI: https://doi.org/10.1090/S0002-9947-1971-0280736-2
- MathSciNet review: 0280736