Symmetric Division of Linear Ordinary Differential Operators

Lixin Du; Manuel Kauers

paper

Symmetric Division of Linear Ordinary Differential Operators

arXiv:2510.01436

Abstract

The symmetric product of two ordinary linear differential operators $L_{1}, L_{2}$ is an operator whose solution set contains the product $f_{1} f_{2}$ of any solution $f_{1}$ of $L_{1}$ and any solution $f_{2}$ of~ $L_{2}$ . It is well known how to compute the symmetric product of two given operators $L_{1}, L_{2}$ . In this paper we consider the corresponding division problem: given a symmetric product $L$ and one of its factors, what can we say about the other factors?