Introduction to Spectral Theory and Inverse Problem on Asymptotically Hyperbolic Manifolds
Hiroshi Isozaki
Broschiertes Buch

Introduction to Spectral Theory and Inverse Problem on Asymptotically Hyperbolic Manifolds

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This manuscript is devoted to a rigorous and detailed exposition of the spectral theory and associated forward and inverse scattering problems for the Laplace-Beltrami operators on asymptotically hyperbolic manifolds. Based upon the classical stationary scattering theory in "n, the key point of the approach is the generalized Fourier transform, which serves as the basic tool to introduce and analyse the time-dependent wave operators and the S-matrix. The crucial role is played by the characterization of the space of the scattering solutions for the Helmholtz equations utilizing a properly defi...