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adjoint approximating sequence assertions BL(R boundary conditions boundary values closure compact support compactness theorem completes the proof cone consequence constant Corollary cp(x data with compact decomposition define denotes dense distribution sense divergence free divergence theorem Doctor of Philosophy equations in free eventually outgoing free space functions with compact gonal graph norm group U(t Hence infinitely differentiable initial data initial value initial value problem iu)m last theorem Lax and Phillips Lemma Lipschitz continuous maximal non-positive boundary Maxwell's equations n x u obstacle obtain orthogonal outgoing and incoming plane previous lemma Proof of Theorem properties prove Lemma real and imaginary satisfy scattering theory skew-adjoint smooth functions square integrable subspaces Suppose tempered distribution translation representation uj(t unitary operators unperturbed group UQ(t value problem vanishes identically wave equation