Fourier integral operators in SG classes II: application to SG hyperbolic Cauchy problems

Here we apply the Fourier Integral Operators calculus developed in a previous paper to the solution of Cauchy problems for a class of hyperbolic linear systems and operators. We require, in particular, that the eigenvalues of the principal part of the symbol of the operator matrix (or the roots of the characteristic equation associated to the operator of order m) satisfy suitable separation conditions at the infinity.