Abstract

We consider a differentiation-invariant subspace W in the Schwartz space \({{C}^{\infty }}(a;b)\) which admits weak spectral synthesis. We obtain the conditions under which W can be represented as the direct (algebraic and topological) sum of its residual subspace and the closed subspace spanned by the set of exponential monomials contained in W.

中文翻译：

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Schwartz 空间的可合成微分不变子空间的表示

摘要

我们考虑Schwartz 空间\({{C}^{\infty }}(a;b)\)中的微分不变子空间W，它允许弱谱合成。我们获得了W可以表示为其残差子空间和由W 中包含的指数单项式集合跨越的闭子空间的直接（代数和拓扑）和的条件。