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arXiv · 2003.03467

Laplace invariants of differential operators

David Hobby·Ekaterina Shemyakova
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Abstract

We identify conditions giving large natural classes of partial differential operators for which it is possible to construct a complete set of Laplace invariants. In order to do that we investigate general properties of differential invariants of partial differential operators under gauge transformations and introduce a sufficient condition for a set of invariants to be complete. We also give a some mild conditions that guarantee the existence of such a set. The proof is constructive. The method gives many examples of invariants previously known in the literature as well as many new examples including multidimensional.

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David Hobby, Ekaterina Shemyakova. 2020-03-06. Laplace invariants of differential operators. https://doi.org/10.1215/00192082-8746137

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