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arXiv · 1212.4265

Failure of the Weierstrass Preparation Theorem in quasi-analytic Denjoy-Carleman rings

Francesca Acquistapace·Fabrizio Broglia·Michail Bronshtein·Andreea Nicoara·Nahum Zobin
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Abstract

It is shown that Denjoy-Carleman quasi-analytic rings of germs of functions in two or more variables fail to satisfy the Weierstrass Preparation Theorem. The result is proven via a non-extension theorem.

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Francesca Acquistapace, Fabrizio Broglia, Michail Bronshtein, Andreea Nicoara, Nahum Zobin. 2014-03-05. Failure of the Weierstrass Preparation Theorem in quasi-analytic Denjoy-Carleman rings. https://doi.org/10.1016/j.aim.2014.03.002

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