Scattering theory of the ppp-form Laplacian on manifolds with generalized cusps (original) (raw)

2014, Journal of Spectral Theory

Scattering theory for p-forms on hyperbolic real space

arXiv: Differential Geometry, 2001

Due to spectral obstructions, a scattering theory in the Lax-Phillips sense for the wave equation for differential p-forms on H^{n+1} cannot be developed. As a consequence, Huygens' principle for the wave equation in this context does not hold. If we restrict the class of forms and we consider the case of coclosed p-forms on H^{n+1}, when n=2p, Huygens' principle does hold and thus in this case incoming and outgoing subspaces can be constructed.

Spectral Analysis of the Laplacian Acting on Discrete Cusps and Funnels

arXiv: Spectral Theory, 2019

We study perturbations of the discrete Laplacian associated to discrete analogs of cusps and funnels. We perturb the metric and the potential in a long-range way. We establish a propagation estimate and a Limiting Absorption Principle away from the possible embedded eigenvalues. The approach is based on a positive commutator technique.

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