Title :

{\L}ojasiewicz ideals in Denjoy-Carleman classes

Author(s) :

Thilliez, Vincent [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Studia Mathematica

Pages :

35-46

Publisher :

Instytut Matematyczny - Polska Akademii Nauk

Publication date :

2013

ISSN :

0039-3223

HAL domain(s) :

Mathématiques [math]/Analyse classique [math.CA]
Mathématiques [math]/Analyse fonctionnelle [math.FA]

English abstract : [en]

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 ...
Show more >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 $\mathcal{C}^\infty$ case have a Denjoy-Carleman counterpart.Show less >

Language :

Anglais

Popular science :

Non

Comment :

12 pages

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL