This article is cited in 3 papers

A hierarchy of generalized invariants for linear partial differential operators

E. A. Kartashova

Johannes Kepler University Linz

Abstract: 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.

Keywords: linear partial differential operator, Beals–Kartashova factorization, generalized invariant, hierarchy of invariants.

Received: 23.09.2005
Revised: 25.11.2005

DOI: 10.4213/tmf1988

 English version: Theoretical and Mathematical Physics, 2006, 147:3, 839–846

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