{\L}ojasiewicz ideals in Denjoy-Carleman classes
Classical Analysis and ODEs
2013-07-23 v2 Functional Analysis
Abstract
The classical notion of {\L}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 {\L}ojasiewicz ideals in terms of properties of a generator. This characterization involves a certain type of estimates that differ from the usual {\L}ojasiewicz inequality. We then show that basic properties of {\L}ojasiewicz ideals in the case have a Denjoy-Carleman counterpart.
Cite
@article{arxiv.1210.6307,
title = {{\L}ojasiewicz ideals in Denjoy-Carleman classes},
author = {Vincent Thilliez},
journal= {arXiv preprint arXiv:1210.6307},
year = {2013}
}
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