Refinement of Two-Factor Factorizations of a Linear Partial Differential Operator of Arbitrary Order and Dimension

Abstract

Given a right factor and a left factor of a Linear Partial Differential Operator (LPDO), under which conditions we can refine these two-factor factorizations into one three-factor factorization? This problem is solved for LPDOs of arbitrary order and number of variables. A more general result for the incomplete factorizations of LPDOs is proved as well.

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References in corpus (3)

• Multiple Factorizations of Bivariate Linear Partial Differential Operators
• Obstacles to the Factorization of Linear Partial Differential Operators into Several Factors
• A Jordan-Hoelder Theorem for Differential Algebraic Groups