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A Refinement of Peetre’s Theorem

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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.

Keywords: peetre theorem; refinement peetre; theorem

Journal Title: Results in Mathematics
Year Published: 2019

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