Abstract
Using generalized Sylvester equation, we first develop a scheme for triangularizing a pseudo-differential system and prove a necessary and sufficient condition for factorizing the system into lower and upper triangular systems (LU factorization) independent of lower order terms. We then investigate simultaneous triangularization of a pair of matrix valued pseudo-differential operators under certain spectral conditions on their principal symbols. We also provide two extension results to real principal type systems using a Levi-like condition on the subprincipal symbol and singular symbol calculus.
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