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Extra info for Spectral and evolution problems. Proceedings 12th Crimean Autumn Mathematical School-Symposium (KROMSH-XII). v. 12

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Ann. Sc. Norm. Super Pisa, 2(1992), pp. 151-218. [2] A. Li and C. Morawetz, Scattering by potential using hyperbolic methods, Math. , 52(1989), 321-328. S. Birman, On the number of eigenvalues in the quantum scattering problem. Mat. Zbornik, 52(1960), pp. 163-166. [4] G. Eskin and J. Ralston, The inverse backscattering problem in three dimensions. Comm. Math. , 124(1989), 169-215. [5] G. Eskin and J. Ralston, Inverse backscattering in two dimensions. Comm. Math. , 138(1991), 451-486. [6] G. Eskin and J.

But even when the potential is not weak the Fourier transform of a scattering amplitude contains essential information of the potential as was shown in [15] and [17] in two dimensions and in [16] and [18] in three and higher dimensions. In a series of papers starting from 1969 Prosser [19] has shown that the inverse backscattering problem has a unique solution assuming the potential has a small enough weighted H¨older norm. Generic uniqueness results for the backscattering problem in two and three dimensions were obtained by Eskin and Relston [4]-[6]: they proved that the nonlinear operator taking the potential to the backscattering data is an analytic local homomorphism on an open and dense set of an appropriate functional space (some subsets of Sobolev’s spaces).

Peterburg Math. J. 8 (1997), no. 6, 931–950. [6] M. G. Krein and Sh. N. Saakyan, Some new results in the theory of resolvents of Hermitian operators, Dokl. Akad. Nauk SSSR 169 (1966), no. 6, 1269–1272, (Russian). Simonov K. , Math. 2. Spectral Theory of Operator Pencils 37 ДВУПАРАМЕТРИЧЕСКИЕ КОСИНУС - ФУНКЦИИ Говоров В. М. НТУУ "Киевский Политехнический Институт", Киев, Украина Keywords: Косинус-функция,условие четности Однопараметрические КОФ или "просто"КОФ впервые были изучены в [1]. Приложения КОФ к теории абстрактных дифференциальных уравнений второго порядка систематически изучены в [2] и [4],что дало значительный толчок развитию теории КОФ.

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