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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. 8 (1946), 1-96. MR 0015185 (7:382d)
- [2]
- N. Levison, On the uniqueness of the potential in a Schrödinger equation for a given asymptotic phase, Danske Vid. Selsk. Mat.-Fys. Medd. 25 (1949); Mat. Tidskr. B (1949), 25-30. MR 0030080 (10:710c)
- [3]
- I. M. Gelfand and B. M. Levitan, On the determination of a differential equation from its spectral function, Dokl. Akad. Nauk SSSR 77 (1951), 557-560; Izv. Akad. Nauk. SSSR Ser. Mat. 15 (1951), 309-360; transl., Amer. Math. Soc. Transl. (2) 1 (1955), 253-304. MR 0073805 (17:489c)
- [4]
- R. Jost and W. Kohn, Construction of a potential from a phase shift, Phys. Rev. 87 (1952), 977-992. MR 0051981 (14:556a)
- [5]
- C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, Method of solving the Korteweg-deVries equation, Phys. Rev. Lett. 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. 14 (1961), 435-445. MR 0135866 (24:B1908)
- [7]
- L. Faddeev, Three-dimensional inverse problem in the quantum theory of scattering, J. Math. Phys. 4 (1963), 72-104.
- [8]
- R. Newton, Inverse Schrödinger scattering in three dimensions, Springer-Verlag, New York, 1989. MR 1029031 (91a:81217)
- [9]
- J. B. Keller, The inverse scattering problem in geoemetrical optics and the design of reflectors, IRE Trans. Antennas and Propagation 7 (1959), 146-149.
- [10]
- R. M. Lewis, Physical optics inverse diffraction, IRE Trans. Antennas and Propagation 17 (1969), 308-314.
- [11]
- L. Nirenberg, The Weyl and Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math. 6 (1953), 337-399. MR 0058265 (15:347b)
- [12]
- R. Radon, Ueber die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten, Ber. Verh. Sächs. Akad. Wiss. Leipzig, Math.-Nat. Kl. 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. 83 (1977), 1227-1270; 84 (1978), 691. MR 0490032 (58:9394a)
- [14]
- P. Deift and E. Trubowitz, Inverse scattering on the line, Comm. Pure Appl. Math. 32 (1979), 121-251. MR 512420 (80e:34011)
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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