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Holomorphic functions on subsets of C
Fridman, Buma L. Ma, Daowei
Fridman, Buma L.
Ma, Daowei
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2013-01
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Analytic functions,Hausdorff dimension,Hartogs property
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Fridman, Buma L.; Ma, Daowei. 2013. Holomorphic functions on subsets of C. -- J. Math. Soc. Japan, v. 65, no.1 (2013), 1-12.
Abstract
Let Gamma be a C-infinity curve in C containing 0; it becomes Gamma(theta) after rotation by angle theta about 0. Suppose a C-infinity function f can be extended holomorphically to a neighborhood of each element of the family {Gamma(theta)}. We prove that under some conditions on Gamma the function f is necessarily holomorphic in a neighborhood of the origin. In case Gamma is a straight segment the well known Bochnak-Siciak Theorem gives such a proof for real analyticity. We also provide several other results related to testing holomorphy property on a family of certain subsets of a domain in C.
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Mathematical Society of Japan
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JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN;v.65: issue1
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0025-5645
1881-1167
1881-1167