We prove a Kotake–Narasimhan type theorem in general ultradifferentiable classes given by weight matrices. In doing so we simultaneously recover and generalize significantly the known results for classes given by weight sequences and weight functions. In particular, we obtain a sharp Kotake–Narasimhan theorem for Beurling classes.

中文翻译：

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一般超微类中的 Kotake-Narasimhan 定理

我们在权重矩阵给出的一般超微类中证明了 Kotake-Narasimhan 型定理。在此过程中，我们同时恢复并显着概括了由权重序列和权重函数给出的类别的已知结果。特别是，我们获得了 Beurling 类的尖锐 Kotake-Narasimhan 定理。