English

{\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 C\mathcal{C}^\infty 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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Final version

R2 v1 2026-06-21T22:26:37.100Z