Analyticity on families of circles

Josip Globevnik

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Analyticity on families of circles

Josip Globevnik

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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.

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BibTeX RIS

Josip Globevnik. 2003-11-14. Analyticity on families of circles. https://arxiv.org/abs/math/0311238

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