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arXiv · 1210.6307

Łojasiewicz ideals in Denjoy-Carleman classes

Vincent Thilliez
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Abstract

The classical notion of Łojasiewicz ideals of smooth functions is studied in the context of non-quasianalytic Denjoy-Carleman classes. In the case of principal ideals, we obtain a characterization of Łojasiewicz ideals in terms of properties of a generator. This characterization involves a certain type of estimates that differ from the usual Łojasiewicz inequality. We then show that basic properties of Łojasiewicz ideals in the $\mathcal{C}^\infty$ case have a Denjoy-Carleman counterpart.

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Vincent Thilliez. 2013-07-22. Łojasiewicz ideals in Denjoy-Carleman classes. https://arxiv.org/abs/1210.6307

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