Parametrix of the mixed problem for the hyperbolic system of first order partial differential equations

<div class="line" id="line-35"> <span style="font-family: Arial;"> A parametrix for the mixed problem for a hyperbolic system in a situation where the bicharacteristics are transversal to the boundary is constructed in the form of a global Fourier integral operator (FIO). So the construction of the parametrix of a mixed problem for second order hyperbolic equations, suggested by J. Chazarain, is extended to hyperbolic systems. The manifold of broken bicharacteristics, supplied with a structure of a homogeneous immersed Lagrangian submanifold, plays the role of the canonical relation for FIO. The symbol of FIO is constructed as an asymptotic sum of smooth sections of certain vector bundles on &complexes;. </span></div>