The main purpose of this book is to give a self-contained synthesis of different results in the domain of symbolic calculus of conormal singularities of semilinear hyperbolic progressing waves.

The authors deal generally with real matrix valued coefficients and with real vector valued solutions, but the complex case is similar. They consider also N x N first order systems rather than high order scalar equations, because the polarization properties of symbols are less natural in the latter case. Moreover, although they assume generally that the real characteristics are simple, the methods can give results for symmetric or symmetrizable first order hyperbolic systems.

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