Estimates and Spectral Asymptotics for Systems with Multiplicities

We consider elliptic and hyperbolic systems with diagonalizable principal part. Characteristics are allowed to have variable multiplicities. Assuming that the characteristics are generic, we give estimates for solutions of a hyperbolic Cauchy problem in $L^p$ spaces. The first and second terms of the spectral asymptotics are obtained for the corresponding elliptic system.