In this article, we will refine Peetre’s theorem on coordinate-free characterisation of partial differential operators by taking into account the order of distributions. We will introduce a new notion of… Click to show full abstract
In this article, we will refine Peetre’s theorem on coordinate-free characterisation of partial differential operators by taking into account the order of distributions. We will introduce a new notion of anisotropic distributions and derive a corresponding variant of the Schwartz kernel theorem in the proof. The results presented here can be easily extended to the case of differentiable manifolds.
               
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