Łojasiewicz ideals in Denjoy-Carleman classes

• Autorzy: Vincent Thilliez
• Języki publikacji: EN

Abstrakty

EN

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 $𝓒^{∞}$ case have a Denjoy-Carleman counterpart.

Kategorie tematyczne

• 46E10: Topological linear spaces of continuous, differentiable or analytic functions
• 26E10: C ∞ -functions, quasi-analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 216
• Numer: 1
• Strony: 35-46

Daty

wydano

2013

Twórcy

autor

Vincent Thilliez

• Laboratoire Paul Painlevé, Mathématiques - Bâtiment M2, Université Lille 1, F-59655 Villeneuve d'Ascq Cedex, France

Identyfikatory

DOI

10.4064/sm216-1-3