Huygens' principle for wave equations on symmetric spaces

DOI10.1016/0022-1236(92)90108-UzbMath0757.58036OpenAlexW2034792965MaRDI QIDQ1193910

Sigurdur Helgason

Publication date: 27 September 1992

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(92)90108-u

zbMATH Keywords

Fourier transformwave equationHuygens' principlePaley-Wiener theoremLaplace-Beltrami operatorsymmetric spaceCartan group

Mathematics Subject Classification ID

Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65) Hyperbolic equations on manifolds (58J45)

Related Items (16)

Huygens' principle in Riemannian symmetric spaces ⋮ \(L^ \infty\)-decay estimations of the spherical mean value on symmetric spaces ⋮ A survey on Huygens' principle ⋮ The wave equation for Dunkl operators ⋮ The Paley-Wiener theorem and the local Huygens' principle for compact symmetric spaces: the even multiplicity case ⋮ Normally hyperbolic operators, the Huygens property and conformal geometry ⋮ Integrability and Huygens' principle on symmetric spaces ⋮ Pointwise Fourier inversion: A wave equation approach ⋮ Support theorem for the fundamental solution to the Schrödinger equation on certain compact symmetric spaces ⋮ The shifted wave equation on non-flat harmonic manifolds ⋮ Scattering on Riemannian Symmetric Spaces and Huygens Principle ⋮ Huygens' principle and integrable systems ⋮ Unnamed Item ⋮ Unnamed Item ⋮ The wave equation on homogeneous trees ⋮ Huygen principle and equipartition of energy for the modified wave equation associated to a generalized radial Laplacian

Cites Work

• The Paley-Wiener theorem for distributions on symmetric spaces
• Huygens' principle and Hadamard's conjecture
• Equipartition of energy for waves in symmetric space
• The surjectivity of invariant differential operators on symmetric spaces. I
• A duality for symmetric spaces with applications to group representations
• Translation representations for the solution of the non-euclidean wave equation
• Radon-Fourier transforms on symmetric spaces and related group representations
• Fundamental Solutions of Invariant Differential Operators on Symmetric Spaces
• Duality and Radon Transform for Symmetric Spaces
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