Symmetric Division of Linear Ordinary Differential Operators
Abstract
The symmetric product of two ordinary linear differential operators L1,L2 is an operator whose solution set contains the product f1f2 of any solution f1 of L1 and any solution f2 of~L2. It is well known how to compute the symmetric product of two given operators L1,L2. 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?
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