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Journals / Hacettepe Journal of Mathematics and Statistics / 2013 / Cilt: 42 - Sayı: 4

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

Gusein Sh GUSEİNOV
Pages
6456–8540
Publication Date
2022-10-18
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

🎯
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:Research 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

GUSEİNOV, G. S. (2022). On the Derivation of Explicit Formulae for Solutions of the Wave Equation in Hyperbolic Space. Hacettepe Journal of Mathematics and Statistics, Cilt: 42 - Sayı: 4, 6456–8540. https://ajindex.com/articles/530394

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References (5)

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  3. Helgason, S. Wave equations on homogeneous spaces, Lecture Notes in Mathematics 1077, 254–287, 1984.
  4. 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.
  5. 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.