A more direct way to the Cauchy problem for effectively hyperbolic operators

Abstract

This paper is devoted to a simpler derivation of energy estimates and a proof of the well-posedness, compared to previously existing ones, for effectively hyperbolic Cauchy problem. One difference is that instead of using the general Fourier integral operator, we only use a change of local coordinates x (of the configuration space) leaving the time variable invariant. Another difference is an efficient application of the Weyl-Hörmander calculus of pseudodifferential operators associated with several different metrics.