A hierarchy of generalized invariants for linear partial differential operators
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We study invariants of linear partial differential operators in two variables under gauge transformations. Using the Beals-Kartashova factorization, we construct a hierarchy of generalized invariants for operators of an arbitrary order. We study the properties of these invariants and give some examples. We also show that the classic Laplace invariants correspond to some particular cases of generalized invariants.
Keywordslinear partial differential operator Beals-Kartashova factorization generalized invariant hierarchy of invariants
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