On the Derivation of Explicit Formulae for Solutions of the Wave Equation in Hyperbolic Space

Yıl 2013, Cilt: 42 Sayı: 4, 1 - 15, 01.04.2013

Gusein Sh. Guseinov

Öz

We offer a new approach to solving the initial value problem for thewave equation in hyperbolic space in arbitrary dimensions. Our approach is based on the spectral analysis of the Laplace-Beltrami operator in hyperbolic space and some structural formulae for rapidlydecreasing functions of this operator.

Anahtar Kelimeler

Hyperbolic space, Laplace-Beltrami operator, wave equation, spectralprojection.

On the Derivation of Explicit Formulae for Solutions of the Wave Equation in Hyperbolic Space

Öz

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Anahtar Kelimeler

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Kaynakça

• Birman, M. S. and Solomjak, M. Z. Spectral Theory of Self-Adjoint Operators in Hilbert Space (Reidel, Dordrecht, 1987).
• Guseinov, G. Sh. Spectral approach to derive representation formulae for solutions of the wave equation, Journal of Applied Mathematics 2012, Article ID 761248, 19 pages, 2012. Helgason, S. Wave equations on homogeneous spaces, Lecture Notes in Mathematics 1077, 254–287, 1984.
• Kipriyanov, I. A. and Ivanov, L. A. The Cauchy problem for the Euler-Poisson-Darboux equation in a symmetric space, Math. USSR Sbornik 52, 41–51, 1985.
• Venkov, A. B. Expansions in automorphic eigenfunctions of the Laplace-Beltrami operator in classical symmetric spaces of rank one and the Selberg trace formula, Proc. Steklov Inst. Math. 125, 6–55, 1973.