On Some Microlocal Properties of the Range of a Pseudo-Differential Operator of Principal Type

The purpose of this paper is to obtain microlocal analogues of results by L. H örmander about inclusion relations between the ranges of first order differential operators with coefficients in $C^\infty$ which fail to be locally solvable. Using similar techniques, we shall study the properties of the range of classical pseudo-differential operators of principal type which fail to satisfy condition $(Ψ)$.

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