Ultradifferentiable functions on lines in $\mathbb {R}^n$
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- by Tejinder Neelon
- Proc. Amer. Math. Soc. 127 (1999), 2099-2104
- DOI: https://doi.org/10.1090/S0002-9939-99-04759-0
- Published electronically: March 16, 1999
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Erratum: Proc. Amer. Math. Soc. 131 (2003), 991-992.
Abstract:
It is well known that a function $f\in C^{\infty }(\mathbb {R}^{n})$ whose restriction to every line in $\mathbb {R}^{n}$ is real analytic must itself be real analytic. In this note we study whether this property of real analytic functions is also possessed by some other subclasses of $C^{\infty }$ functions. We prove that if $f\in C^{\infty }(\mathbb {R}^{n})$ is ultradifferentiable corresponding to a sequence $\{M_{k}\}$ on every line in some ‘uniform way’, then $f$ is ultradifferentiable corresponding to the sequence $\{M_{k}\}.$References
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Bibliographic Information
- Tejinder Neelon
- Affiliation: Department of Mathematics, California State University San Marcos, San Marcos, California 92096-0001
- Email: NEELON@MAILHOST1.CSUSM.EDU
- Received by editor(s): August 28, 1997
- Received by editor(s) in revised form: October 15, 1997
- Published electronically: March 16, 1999
- Communicated by: Theodore W. Gamelin
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2099-2104
- MSC (1991): Primary 30D60; Secondary 46F05
- DOI: https://doi.org/10.1090/S0002-9939-99-04759-0
- MathSciNet review: 1487332