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Book Review
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Book Information
Author(s):
Alexander G. Ramm
Title:
Multidimensional inverse scattering problems
Additional book information:
Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 51, Longman Scientific & Technical, Harlow, 1992, 379 pages, $170.00. ISBN 0-582-05665-9
References:
- [1]
- G. Borg, Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte, Acta Math. \textbf{8} (1946), 1--96.
- [2]
- N. Levison, On the uniqueness of the potential in a Schr\"odinger equation for a given asymptotic phase, Danske Vid. Selsk. Mat.-Fys. Medd. \textbf{25} (1949).
- [3]
- I. M. Gelfand and B. M. Levitan, On the determination of a differential equation from its spectral function, Dokl. Akad. Nauk SSSR \textbf{77} (1951), 557-560.
- [4]
- R. Jost and W. Kohn, Construction of a potential from a phase shift, Phys. Rev. \textbf{87} (1952), 977--992.
- [5]
- C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, Method of solving the Korteweg-deVries equation, Phys. Rev. Lett. \textbf{19} (1967), 1095--1097.
- [6]
- I. Kay and H. E. Moses, A simple verification of the Gelfand-Levitan equation for the three-dimensional scattering problem, Comm. Pure Appl. Math. \textbf{14} (1961), 435--445.
- [7]
- L. Faddeev, Three-dimensional inverse problem in the quantum theory of scattering, J. Math. Phys. \textbf{4} (1963), 72--104.
- [8]
- R. Newton, Inverse Schr\"odinger scattering in three dimensions, Springer-Verlag, New York, 1989.
- [9]
- J. B. Keller, The inverse scattering problem in geoemetrical optics and the design of reflectors, IRE Trans. Antennas and Propagation \textbf{7} (1959), 146--149.
- [10]
- R. M. Lewis, Physical optics inverse diffraction, IRE Trans. Antennas and Propagation \textbf{17} (1969), 308--314.
- [11]
- L. Nirenberg, The Weyl and Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math. \textbf{6} (1953), 337--399.
- [12]
- R. Radon, Ueber die Bestimmung von Funktionen durch ihre Integralwerte l\"angs gewisser Mannigfaltigkeiten, Ber. Verh. S\"achs. Akad. Wiss. Leipzig, Math.-Nat. Kl. \textbf{69} (1917), 262--277.
- [13]
- K. T. Smith, D. C. Solmon, and S. L. Wagner, Practical and mathematical aspects of the problem of reconstructing objects from radiographs, Bull. Amer. Math. Soc. \textbf{83} (1977), 1227--1270.
- [14]
- P. Deift and E. Trubowitz, Inverse scattering on the line, Comm. Pure Appl. Math. \textbf{32} (1979), 121--251.
Additional Information:
Reviewer(s):
Reese T.
Prosser
Review Information:
Journal:
Bull. Amer. Math. Soc.
29
(1993),
139-144.
DOI:
10.1090/S0273-0979-1993-00407-5
PII:
S 0273-0979(1993)00407-5
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