Failure of the Weierstrass preparation theorem in quasi-analytic Denjoy-Carleman rings

DOI10.1016/j.aim.2014.03.002zbMath1292.26069arXiv1212.4265OpenAlexW1978575994MaRDI QIDQ2445837

Michail Bronshtein, Nahum Zobin, Andreea C. Nicoara, Fabrizio Broglia, Francesca Acquistapace

Publication date: 15 April 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.4265

zbMATH Keywords

Weierstrass preparation theoremDenjoy-Carleman ringsWeierstrass division property

Mathematics Subject Classification ID

(C^infty)-functions, quasi-analytic functions (26E10) Rings and algebras of continuous, differentiable or analytic functions (46E25) Analytic algebras and generalizations, preparation theorems (32B05)

Related Items (3)

Solutions of quasianalytic equations ⋮ Ultradifferentiable extension theorems: a survey ⋮ Quantitative tame properties of differentiable functions with controlled derivatives

Cites Work

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• Division par un polynôme hyperbolique
• Interpolation in Non-Quasi-Analytic Classes of Infinitely Differentiable Functions.
• On Universal Moment Problems.

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