Displaying similar documents to “Scattering and resolvent on geometrically finite hyperbolic manifolds with rational cusps”

On the distribution of resonances for some asymptotically hyperbolic manifolds

R. G. Froese, Peter D. Hislop (2000)

Journées équations aux dérivées partielles

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We establish a sharp upper bound for the resonance counting function for a class of asymptotically hyperbolic manifolds in arbitrary dimension, including convex, cocompact hyperbolic manifolds in two dimensions. The proof is based on the construction of a suitable paramatrix for the absolute S -matrix that is unitary for real values of the energy. This paramatrix is the S -matrix for a model laplacian corresponding to a separable metric near infinity. The proof of the upper bound on the...

The radiation field is a Fourier integral operator

Antônio Sá Barreto, Jared Wunsch (2005)

Annales de l’institut Fourier

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We show that the ``radiation field'' introduced by F.G. Friedlander, mapping Cauchy data for the wave equation to the rescaled asymptotic behavior of the wave, is a Fourier integral operator on any non-trapping asymptotically hyperbolic or asymptotically conic manifold. The underlying canonical relation is associated to a ``sojourn time'' or ``Busemann function'' for geodesics. As a consequence we obtain some information about the high frequency behavior of the...