Division of Distributions by Locally Definable Quasianalytic Functions
Volume 58 / 2010
Bulletin Polish Acad. Sci. Math. 58 (2010), 201-208
MSC: 14P15, 46F10, 26E10.
DOI: 10.4064/ba58-3-3
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.
