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The Reduced Wave Equation
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According to Lemma according to Theorem Analogously assume asymptotic behavior boundary surface completely continuous consider constant continuous function continuously differentiable converges uniformly coordinate system defined definition denote differential equation Electromagnetic Waves element F exists exterior to G finite number formulation Green's formula harmonic function Hence Holder condition infinity integral equations interior of G linear space Maxwell equations neighborhood polynomial positive real potential theory proof properties prove Lemma radiation conditions radiation pattern regular region regular surface elements relation represented right hand side satisfies a Holder satisfies the conditions satisfies the differential satisfies the equation satisfies the radiation scalar solution spherical harmonics surface currents surface F surface fields tangential components Theory of Electromagnetic transformation twice continuously differentiable uniformly bounded uniformly with respect uniquely unit sphere vanishes identically vector field wave equation zero