A generalization of Radó's theorem

Volume 80 / 2003

E. M. Chirka Annales Polonici Mathematici 80 (2003), 109-112 MSC: 30C99, 32B15. DOI: 10.4064/ap80-0-7


If ${\mit \Sigma }$ is a compact subset of a domain ${\mit \Omega }\subset {{{\mathbb C}}}$ and the cluster values on $\partial {\mit \Sigma }$ of a holomorphic function $f$ in ${\mit \Omega }\setminus {\mit \Sigma }$, $f'\not \equiv 0$, are contained in a compact null-set for the holomorphic Dirichlet class, then $f$ extends holomorphically onto the whole domain ${\mit \Omega }$.


  • E. M. ChirkaSteklov Mathematical Institute
    Gubkin st. 8
    Moscow, Russia

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