Łojasiewicz ideals in Denjoy–Carleman classes
Volume 216 / 2013
Studia Mathematica 216 (2013), 35-46
MSC: 26E10, 46E10.
DOI: 10.4064/sm216-1-3
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.
