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Arc-quasianalytic functions


Authors: Edward Bierstone, Pierre D. Milman and Guillaume Valette
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
Published electronically: February 26, 2015
MathSciNet review: 3359582
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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.


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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

DOI: https://doi.org/10.1090/S0002-9939-2015-12547-6
Keywords: Quasianalytic, arc-quasianalytic, blowing up, resolution of singularities
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
Article copyright: © Copyright 2015 American Mathematical Society

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