Nils Dencker, Jens Wittsten
Published 2011-08-10, updated 2011-10-04Version 2
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. H\"ormander about inclusion relations between the ranges of first order differential operators with coefficients in $C^\infty$ 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 (\Psi) is known to be equivalent to microlocal solvability.
Comments: Added Theorem 4.7, Corollary 4.8 and Lemma A.4, corrected misprints. The paper has 40 pages
On Some Microlocal Properties of the Range of a Pseudo-Differential Operator of Principal Type
Global Properties for first order differential operators on $\mathbb{T}^{r+1}\times(\mathbb{S}^{3})^s$
Microlocal properties of scattering matrices
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