Analytic continuation on complex lines
Authors:
Joseph A. Cima and Josip Globevnik
Journal:
Proc. Amer. Math. Soc. 85 (1982), 411-413
MSC:
Primary 32D15; Secondary 30B40, 32A40
DOI:
https://doi.org/10.1090/S0002-9939-1982-0656114-3
MathSciNet review:
656114
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Abstract | References | Similar Articles | Additional Information
Abstract: The following extension theorem is proved. Let be an open set containing
, the open unit disc in
, and the point 1. Suppose that
is holomorphic on
, the open unit ball of
, let
and assume that for all
in a neighborhood of
the function
, holomorphic on
, continues analytically into
. Then
continues analytically into a neighborhood of
.
- [1] Salomon Bochner and William Ted Martin, Several Complex Variables, Princeton Mathematical Series, vol. 10, Princeton University Press, Princeton, N. J., 1948. MR 0027863
- [2] Josip Globevnik and Edgar Lee Stout, Highly noncontinuable functions on convex domains, Bull. Sci. Math. (2) 104 (1980), no. 4, 417–434 (English, with French summary). MR 602409
- [3] Walter Rudin, Function theory in the unit ball of 𝐶ⁿ, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1982-0656114-3
Article copyright:
© Copyright 1982
American Mathematical Society