  We establish sharp pointwise kernel estimates and dispersive properties for
the wave equation on noncompact symmetric spaces of general rank. This is
achieved by combining the stationary phase method and the Hadamard parametrix,
and in particular, by introducing a subtle spectral decomposition, which allows
us to overcome a well-known difficulty in higher rank analysis, namely the fact
that the Plancherel density is not a differential symbol in general. As
consequences, we deduce the Strichartz inequality for a large family of
admissible pairs and prove global well-posedness results for the corresponding
semilinear equation with low regularity data as on hyperbolic spaces.

Analysis of PDEs