Guseinov, Gusein Sh. Spectral approach to derive the representation formulae for solutions of the wave equation. (English) Zbl 1251.35042 J. Appl. Math. 2012, Article ID 761248, 19 p. (2012). Summary: 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. Cited in 2 Documents MSC: 35L15 Initial value problems for second-order hyperbolic equations 35C15 Integral representations of solutions to PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation PDF BibTeX XML Cite \textit{G. Sh. Guseinov}, J. Appl. Math. 2012, Article ID 761248, 19 p. (2012; Zbl 1251.35042) Full Text: DOI References: [1] R. Courant and D. Hilbert, Methods of Mathematical Physics. Vol. II, Interscience Publishers, New York, NY, USA, 1962. · Zbl 0099.29504 [2] V. I. Smirnov, A Course of Higher Mathematics, Vol. II, Addison-Wesley, Reading, Mass, USA, 1964. · Zbl 0122.29703 [3] M. S. Birman and M. Z. Solomjak, Spectral Theory of Self-Adjoint Operators in Hilbert Space, Reidel, Dordrecht, The Netherlands, 1987. · Zbl 0744.47017 [4] E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations. Vol. 2, Clarendon Press, Oxford, UK, 1958. · Zbl 0097.27601 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.