## Scattering theory on real hyperbolic spaces and their compact perturbations |

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### Contents

Asymptotic Scattering | 2 |

Real Hyperbolic Spaces | 10 |

Horosphere as a limit of spheres | 12 |

14 other sections not shown

### Common terms and phrases

asymptotics ball B(a belongs to L2 bounded Chapter compact support const constant curvature metric coth defined definition Denote dense differential operator dimensional Dirichlet domain E-form E-orthogonal eigenfunctions eigenvalues energy form equivalent estimate euclidean exists finite follows formula fourier transform Green's function H-norm harmonics of order hence Hilbert space holomorphic horosphere hyperbolic spaces implies inequality infinity inner product integral intial data invariant isometries L2-norm Laplacian Lax and Phillips lemma modified Radon transform multiplier noneuclidean norm null space null vectors orthogonal outgoing and incoming Plancherel Plancherel theorem polar coordinates polynomial Proof properties proves the lemma Radon transform rdrdu real hyperbolic spaces reduced wave equation Rellich respect right hand side satisfies Scattering Matrix Scattering Operator scattering theory Schwartz class solution spectrum spherical harmonics subspaces suffices to show Suppose tempered distributions Theorem 4.2 thesis translation representations unique vanishes wave equation Weyl-invariant zero