Łojasiewicz ideals in Denjoy-Carleman classes

Vincent Thilliez. "Łojasiewicz ideals in Denjoy-Carleman classes." Studia Mathematica 216.1 (2013): 35-46. <http://eudml.org/doc/285546>.

@article{VincentThilliez2013,
abstract = {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 $^\{∞\}$ case have a Denjoy-Carleman counterpart.},
author = {Vincent Thilliez},
journal = {Studia Mathematica},
keywords = {Łojasiewicz ideals; ultradifferentiable functions},
language = {eng},
number = {1},
pages = {35-46},
title = {Łojasiewicz ideals in Denjoy-Carleman classes},
url = {http://eudml.org/doc/285546},
volume = {216},
year = {2013},
}

TY - JOUR
AU - Vincent Thilliez
TI - Łojasiewicz ideals in Denjoy-Carleman classes
JO - Studia Mathematica
PY - 2013
VL - 216
IS - 1
SP - 35
EP - 46
AB - 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 $^{∞}$ case have a Denjoy-Carleman counterpart.
LA - eng
KW - Łojasiewicz ideals; ultradifferentiable functions
UR - http://eudml.org/doc/285546
ER -