{\L}ojasiewicz ideals in Denjoy-Carleman classes
Document type :
Compte-rendu et recension critique d'ouvrage
DOI :
Title :
{\L}ojasiewicz ideals in Denjoy-Carleman classes
Author(s) :
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]
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 >
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
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