Holomorphic extensions from open families of circles

Author:
Josip Globevnik

Journal:
Trans. Amer. Math. Soc. **355** (2003), 1921-1931

MSC (2000):
Primary 30E20

Published electronically:
January 8, 2003

MathSciNet review:
1953532

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Abstract: For a circle write . A continuous function on extends holomorphically from (into the disc bounded by ) if and only if the function defined on has a bounded holomorphic extension into . In the paper we consider open connected families of circles , write , and assume that a continuous function on extends holomorphically from each . We show that this happens if and only if the function defined on has a bounded holomorphic extension into the domain for each open family compactly contained in . This allows us to use known facts from several complex variables. In particular, we use the edge of the wedge theorem to prove a theorem on real analyticity of such functions.

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Additional Information

**Josip Globevnik**

Affiliation:
Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Ljubljana, Slovenia

Email:
josip.globevnik@fmf.uni-lj.si

DOI:
http://dx.doi.org/10.1090/S0002-9947-03-03241-0

Received by editor(s):
July 24, 2002

Published electronically:
January 8, 2003

Dedicated:
Dedicated to Professor Ivan Vidav on the occasion of his eighty-fifth birthday

Article copyright:
© Copyright 2003
American Mathematical Society