Geodesic
Łojasiewicz ideals in Denjoy–Carleman classes
Vincent Thilliez1
1 Laboratoire Paul Painlevé Mathématiques – Bâtiment M2 Université Lille 1 F-59655 Villeneuve d'Ascq Cedex, France
Studia Mathematica, Tome 216 (2013) no. 1, pp. 35-46 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm216-1-3
Keywords: classical notion ojasiewicz ideals smooth functions studied context non quasianalytic denjoy carleman classes principal ideals obtain characterization ojasiewicz ideals terms properties generator characterization involves certain type estimates differ usual ojasiewicz inequality basic properties ojasiewicz ideals mathcal infty have denjoy carleman counterpart

Vincent Thilliez 1

1 Laboratoire Paul Painlevé Mathématiques – Bâtiment M2 Université Lille 1 F-59655 Villeneuve d'Ascq Cedex, France 
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Vincent Thilliez. Łojasiewicz ideals in Denjoy–Carleman classes. Studia Mathematica, Tome 216 (2013) no. 1, pp. 35-46. doi: 10.4064/sm216-1-3

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