  Properties of solutions of generic hyperbolic systems with multiple
characteristics with diagonalizable principal part are investigated. Solutions
are represented as a Picard series with terms in the form of iterated Fourier
integral operators. It is shown that this series is an asymptotic expansion
with respect to smoothness under quite general geometric conditions.
Propagation of singularities and sharp regularity properties of solutions are
obtained. Results are applied to establish regularity estimates for scalar
weakly hyperbolic equations with involutive characteristics. They are also
applied to derive the first and second terms of spectral asymptotics for the
corresponding elliptic systems.
