On a class of 2-microhyperbolic systems (Q1820490)

This paper deals with a class of hyperbolic microdifferential equations with involutory double characteristics. The class was first studied by \textit{R. B. Melrose} and \textit{G. A. Uhlmann} [Duke Math. J. 46, 571-582 (1979; Zbl 0422.58026)] and is called that of involutory refraction. Employing the theory of 2nd microlocalization initiated by M. Kashiwara, the paper gives a sharp theorem concerning the microlocal dependence domain for the equations. More precisely, we apply the theory of microlocal study of sheaves [Astérisque 128] to show a theorem about the propagation of 2nd microlocal singularities and generalize the result of the author [Ann. Inst. Fourier (to appear: Zbl 0607.58041)] to the case of systems of equations. The notion of 2-microhyperbolicity (hyperbolicity in 2nd microlocalization) is given.