论文标题
部分可观测时空混沌系统的无模型预测
Ellipticity and the problem of iterates in Denjoy-Carleman classes
论文作者
论文摘要
1978年，梅蒂维尔（Métivier）表明，当且仅当相对于任何非分析性gevrey类中的差异定理均以$ p $为单位，具有分析系数的差异操作员$ p $是椭圆形的。在本文中，我们将此定理扩展到由强烈非quasiantialtix toge序列给出的Denjoy-Carleman类。证明涉及一种在Denjoy-Carleman类中构建最佳功能的新方法，这可能具有独立的兴趣。此外，我们指出，由重量功能给出的Braun-Meise-Taylor类的类似说明无法保持。这分别表示Denjoy-Carleman类和Braun-Meise-Taylor类的特性有重要的差异。
In 1978 Métivier showed that a differential operator $P$ with analytic coefficients is elliptic if and only if the theorem of iterates holds for $P$ with respect to any non-analytic Gevrey class. In this paper we extend this theorem to Denjoy-Carleman classes given by strongly non-quasianalytic weight sequences. The proof involves a new way to construct optimal functions in Denjoy-Carleman classes, which might be of independent interest. Moreover, we point out that the analogous statement for Braun-Meise-Taylor classes given by weight functions cannot hold. This signifies an important difference in the properties of Denjoy-Carleman classes and Braun-Meise-Taylor classes, respectively.
