Checking real analyticity on surfaces

Jacek Bochnak; János Kollár; Wojciech Kucharz

doi:10.1016/j.matpur.2019.05.008

Checking real analyticity on surfaces

Jacek Bochnak
, János Kollár
, Wojciech Kucharz

Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

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 S² 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.

Original language	English (US)
Pages (from-to)	167-171
Number of pages	5
Journal	Journal des Mathematiques Pures et Appliquees
Volume	133
DOIs	https://doi.org/10.1016/j.matpur.2019.05.008
State	Published - Jan 2020

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

Homogeneous polynomial
Real analytic function
Real analytic manifold

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10.1016/j.matpur.2019.05.008

Cite this

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title = "Checking real analyticity on surfaces",

abstract = "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 S2 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.",

keywords = "Homogeneous polynomial, Real analytic function, Real analytic manifold",

author = "Jacek Bochnak and J{\'a}nos Koll{\'a}r and Wojciech Kucharz",

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year = "2020",

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doi = "10.1016/j.matpur.2019.05.008",

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T1 - Checking real analyticity on surfaces

AU - Bochnak, Jacek

AU - Kollár, János

AU - Kucharz, Wojciech

PY - 2020/1

Y1 - 2020/1

N2 - 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 S2 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.

AB - 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 S2 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.

KW - Homogeneous polynomial

KW - Real analytic function

KW - Real analytic manifold

UR - https://www.scopus.com/pages/publications/85065866380

UR - https://www.scopus.com/pages/publications/85065866380#tab=citedBy

U2 - 10.1016/j.matpur.2019.05.008

DO - 10.1016/j.matpur.2019.05.008

M3 - Article

AN - SCOPUS:85065866380

SN - 0021-7824

VL - 133

SP - 167

EP - 171

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

ER -

Checking real analyticity on surfaces

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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