Bulletin of the Belgian Mathematical Society - Simon Stevin

Quasianalytic ultradifferentiability cannot be tested in lower dimensions

Armin Rainer

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Abstract

We show that, in contrast to the real analytic case, quasianalytic ultradifferentiability can never be tested in lower dimensions. Our results are based on a construction due to Jaffe.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 26, Number 4 (2019), 505-517.

Dates
First available in Project Euclid: 13 December 2019

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1576206353

Digital Object Identifier
doi:10.36045/bbms/1576206353

Mathematical Reviews number (MathSciNet)
MR4042397

Zentralblatt MATH identifier
07167740

Subjects
Primary: 26E10: $C^\infty$-functions, quasi-analytic functions [See also 58C25]
Secondary: 30D60: Quasi-analytic and other classes of functions 46E10: Topological linear spaces of continuous, differentiable or analytic functions 58C25: Differentiable maps

Keywords
Quasianalytic ultradifferentiable class Denjoy--Carleman class Osgood--Hartogs type problem

Citation

Rainer, Armin. Quasianalytic ultradifferentiability cannot be tested in lower dimensions. Bull. Belg. Math. Soc. Simon Stevin 26 (2019), no. 4, 505--517. doi:10.36045/bbms/1576206353. https://projecteuclid.org/euclid.bbms/1576206353


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