Division by Flat Ultradifferentiable Functions and Sectorial Extensions
Copyright policy )Division by Flat Ultradifferentiable Functions and Sectorial Extensions
We consider classes $ \mathcal{A}_M(S) $ of functions holomorphic in an open plane sector $ S $ and belonging to a strongly non-quasianalytic class on the closure of $ S $. In $ \mathcal{A}_M(S) $, we construct functions which are flat at the vertex of $ S $ with a sharp rate of vanishing. This allows us to obtain a Borel-Ritt type theorem for $ \mathcal{A}_M(S) $ extending previous results by Schmets and Valdivia. We also derive a division property for ideals of flat ultradifferentiable functions, in the spirit of a classical $ C^\infty $ result of Tougeron.
Slight update of the published version. The definition of closedness in subsections 4.1 and 4.2 is less restrictive. One minor typo corrected
- University of Lille France
- Laboratoire Paul Painlevé France
Mathematics - Complex Variables, Quasi-analytic and other classes of functions of one complex variable, [MATH] Mathematics [math], non-quasianalyticity, 30D60, ideals of ultradifferentiable functions, factorization of ultradifferentiable germs, Borel-Ritt theorem, Mathematics - Classical Analysis and ODEs, Banach spaces of continuous, differentiable or analytic functions, 30E05, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Spaces of bounded analytic functions of one complex variable, \(C^\infty\)-functions, quasi-analytic functions, 46E15, Complex Variables (math.CV), 30E05; 30D60; 46E15; 26E10, 26E10
Mathematics - Complex Variables, Quasi-analytic and other classes of functions of one complex variable, [MATH] Mathematics [math], non-quasianalyticity, 30D60, ideals of ultradifferentiable functions, factorization of ultradifferentiable germs, Borel-Ritt theorem, Mathematics - Classical Analysis and ODEs, Banach spaces of continuous, differentiable or analytic functions, 30E05, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Spaces of bounded analytic functions of one complex variable, \(C^\infty\)-functions, quasi-analytic functions, 46E15, Complex Variables (math.CV), 30E05; 30D60; 46E15; 26E10, 26E10
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