Analyticity of functions analytic on circles

Let Δ be the open unit disc in C , let p ∈ b Δ , and let f be a continuous function on Δ ¯ which extends holomorphically from each circle in Δ ¯ centered at the origin and from each circle in Δ ¯ which passes through p. Then f is holomorphic on Δ.

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2009-12, Vol.360 (2), p.363-368
Main Author: Globevnik, Josip
Format: Article
Language:English
Subjects:
Analyticity
Analyticity on families of circles
Exact sciences and technology
Functions of a complex variable
Mathematical analysis
Mathematics
Real functions
Sciences and techniques of general use
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Description
Summary:Let Δ be the open unit disc in C , let p ∈ b Δ , and let f be a continuous function on Δ ¯ which extends holomorphically from each circle in Δ ¯ centered at the origin and from each circle in Δ ¯ which passes through p. Then f is holomorphic on Δ.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2009.06.002