Arc-quasianalytic functions
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- by Edward Bierstone, Pierre D. Milman and Guillaume Valette PDF
- Proc. Amer. Math. Soc. 143 (2015), 3915-3925 Request permission
Abstract:
We work with quasianalytic classes of functions. Consider a real-valued function $y = f(x)$ on an open subset $U$ of $\mathbb {R}^n$, which satisfies a quasianalytic equation $G(x,y) = 0$. We prove that $f$ is arc-quasianalytic (i.e., its restriction to every quasianalytic arc is quasianalytic) if and only if $f$ becomes quasianalytic after (a locally finite covering of $U$ by) finite sequences of local blowings-up. This generalizes a theorem of the first two authors on arc-analytic functions.References
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Additional Information
- Edward Bierstone
- Affiliation: Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, ON, Canada M5S 2E4
- Email: bierston@math.toronto.edu
- Pierre D. Milman
- Affiliation: Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, ON, Canada M5S 2E4
- Email: milman@math.toronto.edu
- Guillaume Valette
- Affiliation: Instytut Matematyczny PAN, ul. Św. Tomasza 30, 31-027 Kraków, Poland
- Email: gvalette@impan.pl
- Received by editor(s): February 5, 2014
- Received by editor(s) in revised form: May 9, 2014
- Published electronically: February 26, 2015
- Additional Notes: The authors’ research was supported in part by NSERC grants MRS342058, OGP0009070, and OGP0008949, and by NCN grant 2011/01/B/ST1/03875.
- Communicated by: Franc Forstneric
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 3915-3925
- MSC (2010): Primary 26E10, 32B20, 32S45; Secondary 03C64, 30D60
- DOI: https://doi.org/10.1090/S0002-9939-2015-12547-6
- MathSciNet review: 3359582