# Algebraic surfaces determine analyticity of functions

Ontology type: schema:ScholarlyArticle      Open Access: True

### Article Info

DATE

2021-11-25

AUTHORS ABSTRACT

Let f:X→R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f :X \rightarrow \mathbb {R}$$\end{document} be a function defined on a nonsingular real algebraic set X of dimension at least 3. We prove that f is an analytic (resp. a Nash) function whenever the restriction f|S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f|_{S}$$\end{document} is an analytic (resp. a Nash) function for every nonsingular algebraic surface S⊂X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S \subset X$$\end{document} whose each connected component is homeomorphic to the unit 2-sphere. Furthermore, the surfaces S can be replaced by compact nonsingular algebraic curves in X, provided that dimX≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X \ge 2$$\end{document} and f is of class C∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {C}^{\infty }$$\end{document}. More... »

PAGES

57-63

### Journal

TITLE

Archiv der Mathematik

ISSUE

1

VOLUME

118

### Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00013-021-01660-7

DOI

http://dx.doi.org/10.1007/s00013-021-01660-7

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1143203562

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