Division of Distributions by Locally Definable Quasianalytic Functions

Krzysztof Jan Nowak. "Division of Distributions by Locally Definable Quasianalytic Functions." Bulletin of the Polish Academy of Sciences. Mathematics 58.3 (2010): 201-208. <http://eudml.org/doc/281271>.

@article{KrzysztofJanNowak2010,
abstract = {We demonstrate that the Łojasiewicz theorem on the division of distributions by analytic functions carries over to the case of division by quasianalytic functions locally definable in an arbitrary polynomially bounded, o-minimal structure which admits smooth cell decomposition. Hence, in particular, the principal ideal generated by a locally definable quasianalytic function is closed in the Fréchet space of smooth functions.},
author = {Krzysztof Jan Nowak},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {distribution; o-minimal structure; division of distribution; quasianalytic function},
language = {eng},
number = {3},
pages = {201-208},
title = {Division of Distributions by Locally Definable Quasianalytic Functions},
url = {http://eudml.org/doc/281271},
volume = {58},
year = {2010},
}

TY - JOUR
AU - Krzysztof Jan Nowak
TI - Division of Distributions by Locally Definable Quasianalytic Functions
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2010
VL - 58
IS - 3
SP - 201
EP - 208
AB - We demonstrate that the Łojasiewicz theorem on the division of distributions by analytic functions carries over to the case of division by quasianalytic functions locally definable in an arbitrary polynomially bounded, o-minimal structure which admits smooth cell decomposition. Hence, in particular, the principal ideal generated by a locally definable quasianalytic function is closed in the Fréchet space of smooth functions.
LA - eng
KW - distribution; o-minimal structure; division of distribution; quasianalytic function
UR - http://eudml.org/doc/281271
ER -