Propagation of hypo-analyticity along bicharacteristics
S. Berhanu · Pacific Journal of Mathematics · 1989
It is shown here the hypo-analytic singularities for solutions propagate along the ^characteristics of hypo-analytic differential operators of principal type.This generalizes the well-known similar result for analytic differential operators. Introduction. In [4]Hormander proved a result concerning the propagation of C°° singularities of solutions of Pu = f for a smooth linear partial differential operator P whose leading symbol is real.The analytic version of this question was treated by Hanges in [3].In this paper we prove a similar theorem for what we call hypo-analytic differential operators.The paper is organized as follows.In § 1 we discuss the structures we work in and introduce our operators.In §2 we recall the definition of microlocal hypo-analyticity and give a statement of the main result.§3 discusses the Fourier transform criterion of microlocal hypo-analyticity due to Baouendi, Chang and Treves [1].A theorem concerning this criterion is proved in the same section and then used in the proof of our main result.