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Multidimensional Inverse Scattering Problems (Pitman Monographs & Surveys in Pure & AP)
Multidimensional Inverse Scattering Problems (Pitman Monographs & Surveys in Pure & AP)
Date: 23 May 2011, 21:10

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This book presents in an essentially selfcontained way the theory developed by the author for solving multidimensional inverse scattering problems with fixed-energy data, low-frequency data, numerical approaches to multidimensional inverse problems, related signal processing problems, and characterization of scattering data. A well known inverse scattering and spectral theory for the Sturm-Liouville operator on the semi-axis is presented from a new point of view: the interrelations between various steps in the inversion procedures are examined and various ways are given to prove that the reconstructed potential generates the data with which one started. Some concrete new results are obtained. For example, an infinitely differentiable on the half-axis potential with arbitrary small support is constructed, such that this potential produces infinitely many purely imaginary resonances.

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