Extension of holomorphic mappings from to

Author:
Luiza A. Moraes

Journal:
Proc. Amer. Math. Soc. **118** (1993), 455-461

MSC:
Primary 46G20

DOI:
https://doi.org/10.1090/S0002-9939-1993-1139471-0

MathSciNet review:
1139471

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Abstract: Assuming that is a distinguished locally convex space and is a complete locally convex space, we prove that there exists an open subset of that contains and such that every holomorphic mapping whose restriction is -uniformly continuous for every bounded subset of has a unique holomorphic extension such that is -uniformly continuous for every bounded subset of . We show that in many cases we can take . This is the case when is a locally convex space where every -holomorphic mapping that is bounded in a neighbourhood of the origin is locally bounded.

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DOI:
https://doi.org/10.1090/S0002-9939-1993-1139471-0

Article copyright:
© Copyright 1993
American Mathematical Society