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On discrete inverse scattering problems. II
1.K. M. Case and M. Kac, J. Math. Phys., 14, 594 (1973). In the future we will refer to this paper as I. Most of the proofs omitted here are sketched in the Appendix to I.
2.R. Jost and W. Kohn, Phys. Rev. 87, 977 (1952).
3.I. M. Gelfand and B. M. Levitan, Izv. Akad. Nauk SSSR 15, 309 (1951)
3.[I. M. Gelfand and B. M. Levitan, Am. Math. Soc. Transl. 1, 253 (1956)].
4.See, for example, Z. S. Agranovich and V. A. Marchenko, The Inverse Problem of Scattering Theory (Gordon and Breach, New York, 1963).
5.This is obvious if since is then a finite polynomial in The more general statement will be proved elsewhere.
6.We also obtain an equation when but this gives no information of relevance for our particular question.
7.Actually, of course, this determines all the only up to a common factor. Since, however is given by a ratio of ’s this is immaterial. It can indeed be shown that with our assumption as and then by passing to the limit in Eq. (36), and can therefore be omitted.
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