Wave propagation on Riemannian symmetric spaces
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Let X = G K be a Riemannian symmetric space of the noncompact type and let LX be the Laplace-Beltrami operator on X. We consider on X × R a differential equation of the type LXu = P(∂t)u, where P(∂t) is a second order differential operator in t ε{lunate} R. Using the Radon transform on X we relate Huygens' principle for the solutions u to this equation, to the corresponding question for the solutions v to the equation LAv = (P(∂t) + R)v on a maximal flat subspace A, where R is a certain explicit constant. In particular we conclude that Huygens' principle holds for solutions to the (modified) wave equation on X obtained by letting P(∂t) = ∂t2 - R, when X is odd-dimensional and G has one conjugacy class of Cartan subgroups.
Original language | English |
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Journal | Journal of Functional Analysis |
Volume | 107 |
Issue number | 2 |
Pages (from-to) | 270-278 |
Number of pages | 9 |
ISSN | 0022-1236 |
DOIs | |
Publication status | Published - 1 Aug 1992 |
ID: 304298616