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Suppose that £ 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 £ 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.doi:10.2307/2043559 fatcat:qxatahaakjgmxo5bx7bgwijffi