超可微性的非线性条件。

IF 1.2 2区 数学 Q1 MATHEMATICS
Journal of Geometric Analysis Pub Date : 2021-01-01 Epub Date: 2021-06-19 DOI:10.1007/s12220-021-00718-w
David Nicolas Nenning, Armin Rainer, Gerhard Schindl
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引用次数: 3

摘要

乔里斯的一个重要定理指出,如果函数f的两个相对素数幂为C∞,则函数f为C∞。最近,Thilliez证明了一个类似定理在Roumieu型的Denjoy-Carleman类中成立。我们证明了一个等价于Joris结果的除法性质在各种超可微类中都是有效的。一般来说,它在非拟分析类的所有维度上都成立。在准分析的情况下,我们在一维上有普遍的有效性,但是对于某些准分析类,我们在所有维度上也有有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Nonlinear Conditions for Ultradifferentiability.

A remarkable theorem of Joris states that a function f is C if two relatively prime powers of f are C . Recently, Thilliez showed that an analogous theorem holds in Denjoy-Carleman classes of Roumieu type. We prove that a division property, equivalent to Joris's result, is valid in a wide variety of ultradifferentiable classes. Generally speaking, it holds in all dimensions for non-quasianalytic classes. In the quasianalytic case we have general validity in dimension one, but we also get validity in all dimensions for certain quasianalytic classes.

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来源期刊
CiteScore
2.00
自引率
9.10%
发文量
290
审稿时长
3 months
期刊介绍: JGA publishes both research and high-level expository papers in geometric analysis and its applications. There are no restrictions on page length.
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