Obstacles to the Factorization of Linear Partial Differential Operators into Several Factors

Details Obstacles to the Factorization of Linear Partial Differential Operators into Several Factors Obstacles to the Factorization of Linear Partial Differential Operators into Several Factors

2010-10-13

arxiv.org/abs/1010.2652v1

Programming and Computer Software, vol.33, no.2, pp.67-73, 2007

Mathematics

Analysis of PDEs

Scientific paper

We consider algorithms for the factorization of linear partial differential operators. We introduce several new theoretical notions in order to simplify such considerations. We define an obstacle and a ring of obstacles to factorizations. We derive some interesting facts about the new objects, for instance, that they are invariant under gauge transformations. An important theorem for the construction of factoring algorithms is proved: a factorization is defined uniquely from a certain moment on. For operators of orders three and two, obstacles are found explicitly.

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