Normal forms for ordinary differential operators, II

TL;DR

This paper extends the theory of normal forms for non-commuting differential operators and provides a criterion for their commutativity within the Weyl algebra, building on previous work.

Contribution

It introduces an extended framework for normal forms of differential operators and establishes a new commutativity criterion in the Weyl algebra.

Findings

Extended normal form theory for non-commuting operators

A new criterion for operator commutativity in the Weyl algebra

Application of normal forms to differential operator analysis

Abstract

In this paper, which is a follow-up of our first paper "Normal forms for ordinary differential operators, I", we extend the theory of normal forms for non-commuting operators, and obtain as an application a commutativity criterion for operators in the Weyl algebra or, more generally, in the ring of ordinary differential operators, which we prove in the case when operators have a normal form with the restriction top line (for details see Introduction).