  Dispersive and Strichartz estimates for solutions to general strictly
hyperbolic partial differential equations with constant coefficients are
considered. The global time decay estimates of $L^p-L^q$ norms of propagators
are obtained, and it is shown how the time decay rates depend on the geometry
of the problem. The frequency space is separated in several zones each giving a
certain decay rate. Geometric conditions on characteristics responsible for the
particular decay are identified and investigated. Thus, a comprehensive
analysis is carried out for strictly hyperbolic equations of high orders with
lower order terms of a general form. Results are applied to establish time
decay estimates for the Fokker-Planck equation and for semilinear hyperbolic
equations.
