Analyticity of functions analytic on circles

2009/06/06 by Josip Globevnik, Globevnik, Josip
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #math.CV

paper · pdf · doi:10.48550/arxiv.0906.1295

9 pages, to appear in Journ.Math.Anal.Appl

arxiv created 2009/06/06 · arxiv updated 2009/12/01

Abstract

Let U be the closed unit disc in C and let p be a point on the unit circle. Let f be a continuous function on U which extends holomorphically from each circle contained in U and centered at the origin, and from each circle contained in U and passing through the point p. Then f is holomorphic in the interior of U.

Related

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• Analyticity on families of circles
• A decomposition of functions with zero means on circles
• A Morera type theorem in the strip
• Holomorphic functions on subsets of C