Geodesic
Division of Distributions by Locally Definable Quasianalytic Functions
Krzysztof Jan Nowak1
1 Institute of Mathematics Jagiellonian University Łojasiewicza 6 30-348 Kraków, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) no. 3, pp. 201-208

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ba58-3-3
Keywords: demonstrate ojasiewicz theorem division distributions analytic functions carries division quasianalytic functions locally definable arbitrary polynomially bounded o minimal structure which admits smooth cell decomposition hence particular principal ideal generated locally definable quasianalytic function closed chet space smooth functions

Krzysztof Jan Nowak 1

1 Institute of Mathematics Jagiellonian University Łojasiewicza 6 30-348 Kraków, Poland 
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Krzysztof Jan Nowak. Division of Distributions by Locally
 Definable Quasianalytic Functions. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) no. 3, pp. 201-208. doi: 10.4064/ba58-3-3

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