Unitary One-Parameter Groups with Finite speed of Propagation

Abstract

Suppose that $\xi$ is a Hermitian vector bundle over a Riemannian manifold and that $U$ is a one-parameter group of linear operators on the set of smooth sections of $\xi$ with compact support. We prove that if $U$ satisfies a smoothness condition, is unitary, and propagates initial data with finite speed, then it can be constructed from the solutions of a first-order symmetric hyperbolic system of partial differential equations.