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dc.contributor.authorFridman, Buma L.
dc.contributor.authorMa, Daowei
dc.date.accessioned2013-06-26T16:26:56Z
dc.date.available2013-06-26T16:26:56Z
dc.date.issued2013-01
dc.identifier.citationFridman, Buma L.; Ma, Daowei. 2013. Holomorphic functions on subsets of C. -- J. Math. Soc. Japan, v. 65, no.1 (2013), 1-12.en_US
dc.identifier.issn0025-5645
dc.identifier.issn1881-1167
dc.identifier.otherWOS:000319025400001
dc.identifier.urihttp://hdl.handle.net/10057/5800
dc.identifier.urihttp://dx.doi.org/10.2969/jmsj/06510001
dc.descriptionClick on the DOI link to access the article (may not be free).en_US
dc.description.abstractLet 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.en_US
dc.language.isoen_USen_US
dc.publisherMathematical Society of Japanen_US
dc.relation.ispartofseriesJOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN;v.65: issue1
dc.subjectAnalytic functionsen_US
dc.subjectHausdorff dimensionen_US
dc.subjectHartogs propertyen_US
dc.subject.classificationMathematics
dc.titleHolomorphic functions on subsets of Cen_US
dc.typeArticleen_US
dc.description.versionPeer reviewed
dc.rights.holder2013 © Mathematical Society of Japan


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