Łojasiewicz ideals in Denjoy–Carleman classes

Tom 216 / 2013

Vincent Thilliez Studia Mathematica 216 (2013), 35-46 MSC: 26E10, 46E10. DOI: 10.4064/sm216-1-3

Streszczenie

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.

Autorzy

  • Vincent ThilliezLaboratoire Paul Painlevé
    Mathématiques – Bâtiment M2
    Université Lille 1
    F-59655 Villeneuve d'Ascq Cedex, France
    e-mail

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