On the Microlocal Properties of the Range of Systems of Principal Type

The purpose of this paper is to study microlocal conditions for inclusion relations between the ranges of square systems of pseudodifferential operators which fail to be locally solvable. The work is an extension of earlier results for the scalar case in this direction, where analogues of results by L. Hörmander about inclusion relations between the ranges of first order differential operators with coefficients in C ^∞ which fail to be locally solvable were obtained. We shall study the properties of the range of systems of principal type with constant characteristics for which condition (Ψ) is known to be equivalent to microlocal solvability.