Analyticity on families of circles

Details Analyticity on families of circles Analyticity on families of circles

2003-11-14

arxiv.org/abs/math/0311238v1

Mathematics

Complex Variables

Scientific paper

It is known that if f is a continuous function on the complex plane which
extends holomorphically from each circle surrounding the origin then f is not
necessarily holomorphic. In the paper we prove that if, in addition, f extends
holomorphically from each circle belonging to an open family of circles which
do not surround the origin then f is holomorphic.

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