Analyticity on families of circles
Abstract
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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- November 2003
- DOI:
- arXiv:
- arXiv:math/0311238
- Bibcode:
- 2003math.....11238G
- Keywords:
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- Complex Variables