Sharpness and the local Petrovskii condition for strictly hyperbolic operators with constant coefficients

It is proved that for almost all hyperbolic operators with constant coefficients analytic sharpness of the fundamental solution everywhere is equivalent to the local Petrovskii condition. In the proximity of simple ($O$-modal) singularities of wave front sets the author finds all domains from one side of which there is sharpness.
Bibliography: 24 titles.