Resonance expansions for tensor-valued waves on asymptotically Kerr-de Sitter spaces

作者：Hintz Peter

来源：Journal of Spectral Theory, 2017, 7(2): 519-557.

DOI：10.4171/JST/171

• Non-scalar waves
• normally hyperbolic trapping
• high energy estimates
• analytic continuation
• pseudodifferential inner products

In recent joint work with Andras Vasy [2 5], we analyze the low energy behavior of differential form-valued waves on black hole spacetimes. In order to deduce asymptotics and decay from this, one in addition needs high energy estimates for the wave operator acting on sections of the form bundle. The present paper provides these on perturbations of Schwarzschild-de Sitter spaces in all spacetime dimensions n >= 4. In fact, we prove exponential decay, up to a finite-dimensional space of resonances, of waves valued in any finite rank subbundle of the tensor bundle, which in particular includes differential forms and symmetric tensors. As the main technical tool for working on vector bundles that do not have a natural positive definite inner product, we introduce pseudodifferential inner products, which are inner products depending on the position in phase space.

• 出版日期2017