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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 42 Issue: 4

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

Gusein Sh. Guseinov
Pages
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Publication Date
2013-04-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

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Objective & Hypothesis:We offer a new approach to solving the initial value problem for thewave equation in hyperbolic space in arbitrary dimensions.
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Key Findings & Data:We offer a new approach to solving the initial value problem for thewave equation in hyperbolic space in arbitrary dimensions.
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Conclusion & Impact: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.
🔬Design:Article
📍Scope:Comprehensive Sample
⚙️Variables:Hyperbolic space · Laplace-Beltrami operator · wave equation

Abstract

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.

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Cite This Article

Guseinov, G. S. (2013). On the Derivation of Explicit Formulae for Solutions of the Wave Equation in Hyperbolic Space. Hacettepe Journal of Mathematics and Statistics, Volume: 42 Issue: 4. https://ajindex.com/articles/1403467

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References (4)

  1. Birman, M. S. and Solomjak, M. Z. Spectral Theory of Self-Adjoint Operators in Hilbert Space (Reidel, Dordrecht, 1987).
  2. 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.
  3. 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.
  4. 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.