# Huygens' principle for wave equations on symmetric spaces

- Authors
- Journal
- Journal of Functional Analysis 0022-1236
- Publisher
- Elsevier
- Publication Date
- Volume
- 107
- Issue
- 2
- Identifiers
- DOI: 10.1016/0022-1236(92)90108-u
- Disciplines

## Abstract

Abstract Let X = G K be a symmetric space, L X the Laplace-Betrami operator on X, and 2ϱ the sum of the positive restricted roots of X (with multiplicity). Using the Fourier transform on X we write down the solution of the modified wave equation ∂ 2u ∂t 2 = (L X + ¦ϱ¦ 2)u on X . It is proved, using the Paley-Wiener theorem for this Fourier transform ( S. Helgason, Ann. of Math. 98 (1973), 451–480) that the equation satisfies Huygens' principle if dim X is odd and all Cartan subgroups of G are conjugate.

## There are no comments yet on this publication. Be the first to share your thoughts.