Differential operators with simple characteristics
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In view of Theorem 3.3.7, the results of Chapter VII give an existence theory for every differential operator with simple real characteristics and constant coefficients in the principal part. We shall prove in this chapter that the latter hypothesis can be replaced by a strengthened form of the necessary condition for existence of solutions given in Theorem 6.1.1 (see section 8.7). Weaker existence theorems for such operators have been given before by Hörmander , .
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