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) |
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Pages (from-to) | 167-171 |
Number of pages | 5 |
Journal | Journal des Mathematiques Pures et Appliquees |
Volume | 133 |
DOIs | |
State | Published - Jan 2020 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics
Keywords
- Homogeneous polynomial
- Real analytic function
- Real analytic manifold