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arXiv · 1606.07824

Malgrange division by quasianalytic functions

Edward Bierstone·Pierre D. Milman
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Abstract

Quasianalytic classes are classes of infinitely differentiable functions that satisfy the analytic continuation property enjoyed by analytic functions. Two general examples are quasianalytic Denjoy-Carleman classes (of origin in the analysis of linear partial differential equations) and the class of infinitely differentiable functions that are definable in a polynomially bounded o-minimal structure (of origin in model theory). We prove a generalization to quasianalytic functions of Malgrange's celebrated theorem on the division of infinitely differentiable by real-analytic functions.

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Edward Bierstone, Pierre D. Milman. 2016-06-24. Malgrange division by quasianalytic functions. https://doi.org/10.1112/jlms.12032

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