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Journal of Applied Mathematics
Volume 2012, Article ID 761248, 19 pages
http://dx.doi.org/10.1155/2012/761248
Research Article

Spectral Approach to Derive the Representation Formulae for Solutions of the Wave Equation

Department of Mathematics, Atilim University, Incek, 06836 Ankara, Turkey

Received 28 September 2011; Accepted 30 January 2012

Academic Editor: Pablo González-Vera

Copyright © 2012 Gusein Sh. Guseinov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.