平坦超可微函数的除法与扇形扩张
Division by Flat Ultradifferentiable Functions and Sectorial Extensions
摘要：
我们考虑开平面扇区$ S $中全纯的函数类$ \mathcal{A}_M(S) $，并且在$ S $的闭包上属于强非拟解析类.在$ \mathcal{A}_M(S) $中，我们构造了在$ S $的顶点处平坦的函数，并且具有急剧的消失率。这使我们能够获得一个Borel-Ritt型定理的$ \mathcal{A}_M(S) $扩展以前的结果Schmets和Valdivia。我们还得到了一个部门的理想平坦的超可微函数的性质，在一个经典的$ C^\infty $结果Tougeron的精神。
英文摘要：
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.
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