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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba58-3-3,
author = {Krzysztof Jan Nowak},
title = {Division of Distributions by Locally Definable Quasianalytic Functions},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {58},
year = {2010},
pages = {201-208},
zbl = {1211.14061},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba58-3-3}
}
Krzysztof Jan Nowak. Division of Distributions by Locally Definable Quasianalytic Functions. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) pp. 201-208. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba58-3-3/