{\L}ojasiewicz ideals in Denjoy-Carleman classes
Type de document :
Compte-rendu et recension critique d'ouvrage
DOI :
Titre :
{\L}ojasiewicz ideals in Denjoy-Carleman classes
Auteur(s) :
Titre de la revue :
Studia Mathematica
Pagination :
35-46
Éditeur :
Instytut Matematyczny - Polska Akademii Nauk
Date de publication :
2013
ISSN :
0039-3223
Discipline(s) HAL :
Mathématiques [math]/Analyse classique [math.CA]
Mathématiques [math]/Analyse fonctionnelle [math.FA]
Mathématiques [math]/Analyse fonctionnelle [math.FA]
Résumé en anglais : [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 ...
Lire la suite >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.Lire moins >
Lire la suite >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.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
Commentaire :
12 pages
Collections :
Source :
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