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If Σ is a compact subset of a domain Ω ⊂ ℂ and the cluster values on ∂Σ of a holomorphic function f in Ω∖Σ, f' ≢ 0, are contained in a compact null-set for the holomorphic Dirichlet class, then f extends holomorphically onto the whole domain Ω.
E. M. Chirka. "A generalization of Radó's theorem." Annales Polonici Mathematici 80.1 (2003): 109-112. <http://eudml.org/doc/280687>.
@article{E2003, abstract = {If Σ is a compact subset of a domain Ω ⊂ ℂ and the cluster values on ∂Σ of a holomorphic function f in Ω∖Σ, f' ≢ 0, are contained in a compact null-set for the holomorphic Dirichlet class, then f extends holomorphically onto the whole domain Ω.}, author = {E. M. Chirka}, journal = {Annales Polonici Mathematici}, keywords = {holomorphic extensions; Cantor set; analytic capacity}, language = {eng}, number = {1}, pages = {109-112}, title = {A generalization of Radó's theorem}, url = {http://eudml.org/doc/280687}, volume = {80}, year = {2003}, }
TY - JOUR AU - E. M. Chirka TI - A generalization of Radó's theorem JO - Annales Polonici Mathematici PY - 2003 VL - 80 IS - 1 SP - 109 EP - 112 AB - If Σ is a compact subset of a domain Ω ⊂ ℂ and the cluster values on ∂Σ of a holomorphic function f in Ω∖Σ, f' ≢ 0, are contained in a compact null-set for the holomorphic Dirichlet class, then f extends holomorphically onto the whole domain Ω. LA - eng KW - holomorphic extensions; Cantor set; analytic capacity UR - http://eudml.org/doc/280687 ER -