Spectral Approach To Derive the Representation Formulae for Solutions of the Wave Equation
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2012
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Hindawi Publishing Corporation
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Using spectral properties of the Laplace operator and some structural formula for rapidly decreasing functions of the Laplace operator, we offer a novel method to derive explicit formulae for solutions to the Cauchy problem for classical wave equation in arbitrary dimensions. Among them are the well-known d'Alembert, Poisson, and Kirchhoff representation formulae in low space dimensions.
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