Introduction To Spectral Theory And Inverse Problem On Asymptotically Hyperbolic Manifolds
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A01=Hiroshi Isozaki
Author_Hiroshi Isozaki
Boundary Control Method
Category=PBML
Dirichlet-to-Neumann Map
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Hyperbolic Manifolds
Inverse Problems
S-matrix
Scattering Theory
Product details
- ISBN 9784864970211
- Publication Date: 01 Aug 2014
- Publisher: Mathematical Society of Japan
- Publication City/Country: JP
- Product Form: Paperback
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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 ℝn, 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 defined Besov-type space. After developing the scattering theory, we describe, for some cases, the inverse scattering on the asymptotically hyperbolic manifolds by adopting, for the considered case, the boundary control method for inverse problems.The manuscript is aimed at graduate students and young mathematicians interested in spectral and scattering theories, analysis on hyperbolic manifolds and theory of inverse problems. We try to make it self-consistent and, to a large extent, not dependent on the existing treatises on these topics. To our best knowledge, it is the first comprehensive description of these theories in the context of the asymptotically hyperbolic manifolds.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets
