dc.contributor.author Bochnak, Jacek dc.contributor.author Kucharz, Wojciech dc.date.accessioned 2018-11-06T07:08:51Z dc.date.available 2018-11-06T07:08:51Z dc.date.issued 2018-11-05 dc.identifier.uri http://publications.mfo.de/handle/mfo/1390 dc.description.abstract We prove that a real-valued function on a real analytic manifold is analytic whenever all its restrictions to $2$-dimensional analytic submanifolds are analytic functions. We also obtain analogous results in the framework of Nash manifolds and nonsingular real algebraic sets. These results can be regarded as substitutes in the real case for the classical theorem of Hartogs, asserting that a complex-valued function defined on an open subset of $C^n$ is holomorphic if it is holomorphic with respect to each variable separately. In the proofs we use methods of real algebraic geometry even though the initial problem is purely analytic. en_US dc.language.iso en_US en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2018,23 dc.subject Real analytic manifold en_US dc.subject Analytic function en_US dc.subject Nash manifold en_US dc.subject Nash function en_US dc.subject Real algebraic set en_US dc.subject Regular function en_US dc.title Real Analyticity is Concentrated in Dimension 2 en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2018-23 local.scientificprogram Research in Pairs 2018 en_US local.series.id OWP-2018-23 en_US local.subject.msc 32 en_US local.subject.msc 58 en_US local.subject.msc 14 en_US
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