Analyticity on families of circles
classification
🧮 math.CV
keywords
circlecirclesextendsholomorphicholomorphicallyoriginthenaddition
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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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