Lojasiewicz ideals in denjoy-carleman classes

摘要

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