Division of Distributions by Locally Definable Quasianalytic Functions

Volume 58 / 2010

Krzysztof Jan Nowak Bulletin Polish Acad. Sci. Math. 58 (2010), 201-208 MSC: 14P15, 46F10, 26E10. DOI: 10.4064/ba58-3-3


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.


  • Krzysztof Jan NowakInstitute of Mathematics
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland

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