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dc.contributor.authorBochnak, Jacek
dc.contributor.authorKucharz, Wojciech
dc.date.accessioned2018-11-06T07:08:51Z
dc.date.available2018-11-06T07:08:51Z
dc.date.issued2018-11-05
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1390
dc.description.abstractWe 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.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2018,23
dc.subjectReal analytic manifolden_US
dc.subjectAnalytic functionen_US
dc.subjectNash manifolden_US
dc.subjectNash functionen_US
dc.subjectReal algebraic seten_US
dc.subjectRegular functionen_US
dc.titleReal Analyticity is Concentrated in Dimension 2en_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2018-23
local.scientificprogramResearch in Pairs 2018en_US
local.series.idOWP-2018-23en_US
local.subject.msc32en_US
local.subject.msc58en_US
local.subject.msc14en_US


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