We prove that the Hermite functions are an absolute Schauder basis for many global weighted spaces of ultradifferentiable functions in the matrix weighted setting and we determine also the corresponding coefficient spaces, thus extending the previous work by Langenbruch. As a consequence, we give very general conditions for these spaces to be nuclear. In particular, we obtain the corresponding results for spaces defined by weight functions.

中文翻译：

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矩阵加权设置中超微函数的核全局空间


我们证明 Hermite 函数是矩阵加权设置中超微函数的许多全局加权空间的绝对 Schauder 基，并且我们还确定了相应的系数空间，从而扩展了 Langenbruch 之前的工作。因此，我们为这些空间成为核空间提供了非常一般的条件。特别是，我们获得了由权函数定义的空间的相应结果。