Literature cited
V. G. Tarnopol'skii, “Scattering problem for difference equation,” Dokl. Akad. Nauk SSSR,136, No. 4 (1961).
Yu. M. Berezanskii, Eigenfunction Expansion of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).
Yu. M. Berezenskii, “Review of the spectral theory of self-adjoint differential and difference operators inl 2-space,” Proceedings of Seminar on Functional Analysis [in Russian], No. 2, Institute of Mathematics of the Academy of Sciences of the UkrSSR, Kiev (1970).
K. M. Case and M. Kac, “A discrete version of the inverse scattering problem,” J. of Math. Phys.,14, No. 5, 594–603 (1973).
K. M. Case, “On discrete scattering problems,” J. of Math. Phys.,14, No. 7, 916–920 (1973).
K. M. Case and S. C. Chiu, “The discrete version of the Marchenco equations in the inverse scattering problem,” J. of Math. Phys.,14, No. 11, 1643–1647 (1973).
A. Ya. Povzner, “On the expansion of arbitrary function in eigenfunctions of the operator Δu + cu,” Mat. Sb.,32(74), No. 1 (1953).
L. P. Nizhnik, “Scattering problem for one Schrödinger equation,” Ukr. Mat. Zh.,12, No. 2 (1960).
yu. M. Berezenskii, “On the uniqueness theorem in the inverse problem of spectral analysis for Schrödinger equation,” Proc. Moscow Math. Soc.,7 (1958).
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Translated from Ukraiaskii Matematicheskii Zhuraal, Vol. 28, No. 3, pp. 342–351, May–June, 1976.
In conclusion the author expresses gratitude to Yu. M. Berezanskii for attention to the work.
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Tarnopol'skii, V.G. The scattering problem for difference equation with operator coefficients. Ukr Math J 28, 265–273 (1976). https://doi.org/10.1007/BF01089173
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DOI: https://doi.org/10.1007/BF01089173