Mathematics > Classical Analysis and ODEs
[Submitted on 3 Dec 2018]
Title:Checking real analyticity on surfaces
View PDFAbstract:We prove that a real-valued function (that is not assumed to be continuous) on a real analytic manifold is analytic whenever all its restrictions to analytic submanifolds homeomorphic to the 2-sphere are analytic. This is a real analog for the classical theorem of Hartogs that a function on a complex manifold is complex analytic iff it is complex analytic when restricted to any complex curve.
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