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Introduction to spectral theory and inverse problem on asymptotically hyperbolic manifolds

Introduction to spectral theory and inverse problem on asymptotically hyperbolic manifolds

Chapter 1. Fourier transforms on the hyperbolic space 1. Basic geometry in the hyperbolic space 2. Besov type spaces 3. 1-dimensional problem 4. The upper-half space model 5. Modified Radon transform 6. Radon transform and the wave equation Chapter 2. Perturbation of the metric 1. Preliminaries from elliptic partial differential …