Uniqueness in the spacelike Cauchy problem..and precise finite speed for symmetrisable..hyperbolic operators...

Abstract. For operators symmetrisable by a pseudodifferential operator in x, there is uniqueness in the Cauchy problem at arbitrary spacelike surface and precise finite speed described by influence curves. UCP is a consequence of finite speed. Finite speed is proved direction by direction with estimates for regularized operators proved using refined calculi of Beals-Fefferman- Hormander.