We offer a new approach to spectral synthesis on affine groups. The idea is to consider solution spaces of systems of linear partial differential equations corresponding to invariant differential operators with respect to some closed subgroup of the general linear group on $$\mathbb{R}^n$$ R n . We show that a certain type of spherical spectral analysis and spectral synthesis holds for such solution spaces.

中文翻译：

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光谱合成和偏微分方程

我们提供了一种新的仿射群光谱合成方法。这个想法是考虑相对于 $$\mathbb{R}^n$$ R n 上的一般线性群的某个封闭子群的线性偏微分方程系统的解空间，这些方程对应于不变微分算子。我们表明某种类型的球面谱分析和谱合成适用于这种解空间。