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The scattering problem for difference equation with operator coefficients. (English) Zbl 0342.39004

MSC:

39A10 Additive difference equations
47A40 Scattering theory of linear operators
Full Text: DOI

References:

[1] V. G. Tarnopol’skii, ?Scattering problem for difference equation,? Dokl. Akad. Nauk SSSR,136, No. 4 (1961).
[2] Yu. M. Berezanskii, Eigenfunction Expansion of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).
[3] 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).
[4] K. M. Case and M. Kac, ?A discrete version of the inverse scattering problem,? J. of Math. Phys.,14, No. 5, 594-603 (1973). · doi:10.1063/1.1666364
[5] K. M. Case, ?On discrete scattering problems,? J. of Math. Phys.,14, No. 7, 916-920 (1973). · doi:10.1063/1.1666417
[6] 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). · doi:10.1063/1.1666237
[7] A. Ya. Povzner, ?On the expansion of arbitrary function in eigenfunctions of the operator ?u + cu,? Mat. Sb.,32(74), No. 1 (1953).
[8] L. P. Nizhnik, ?Scattering problem for one Schrödinger equation,? Ukr. Mat. Zh.,12, No. 2 (1960). · Zbl 0098.29802
[9] 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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