ojasiewicz ideals in Denjoy-Carleman classes
Abstract
The classical notion of ojasiewicz 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 ojasiewicz ideals in terms of properties of a generator. This characterization involves a certain type of estimates that differ from the usual ojasiewicz inequality. We then show that basic properties of ojasiewicz ideals in the C∞ case have a Denjoy-Carleman counterpart.
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