Abstract
We consider classes \({cal A}\) 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 \({cal A}\) 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 \({cal A}\) 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 ∞ result of Tougeron.
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Thilliez, V. Division by Flat Ultradifferentiable Functions and Sectorial Extensions. Results. Math. 44, 169–188 (2003). https://doi.org/10.1007/BF03322923
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DOI: https://doi.org/10.1007/BF03322923