Introduction to spectral theory and inverse problem on asymptotically hyper blic manifolds Isozaki, Hiroshi

By:

Isozaki, Hiroshi

Series: MSJ Memoirs Monographs series, Vol.32, 2014Publication details: Japan Mathematical Society of Japan 2014Description: vii, 251 pISBN:

9784864970211

Subject(s):

DDC classification:

517.7 I8I6

Summary: 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. (http://mathsoc.jp/publication/memoir/memoirs-e.html)

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Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
Book	Ahmedabad	Non-fiction	517.7 I8I6 (Browse shelf(Opens below))	Available		186624

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	516.35 A7G3 Geometric algebra	517.6 M6I6 Interval analysis	517.7 I8I6 Introduction to spectral theory and inverse problem on asymptotically hyper blic manifolds	518 A2 Advanced techniques in applied mathematics	518 C8I6 Information theory: coding theorems for discrete memoryless systems	518 F2C6 A concise introduction to numerical analysis	Next

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.
(http://mathsoc.jp/publication/memoir/memoirs-e.html)

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