Jost Solution of the Matrix Difference Equations
DOI:
https://doi.org/10.5644/SJM.06.1.06Keywords:
Discrete operator, spectral analysis, non-selfadjoint operator, Jost solutionAbstract
In this paper, we investigate the Jost solution and the analytical properties of the Jost solution of the non-selfadjoint matrix difference equation of second order.
2000 Mathematics Subject Classification. 39A70, 47A10, 47B39
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References
M. Adıvar and E. Bairamov, Spectral properties of non-selfadjoint difference operators, J. Math. Anal. Appl., 261 (2001), 461–478.
M. Adıvar and E. Baramov, Difference equations of second order with spectral singularities, J. Math. Anal. Appl., 277 (2003), 714–721.
E. Bairamov, O. Cakar and A. M. Krall, ¨ An eigenfuction expansion for a pencil of a Schr¨odinger operator with spectral singularities, J. Differ. Equations, 151 (1999), 268–289.
E. Bairamov, O. Cakar and A. M. Krall, ¨ Non-selfadjoint difference operators and Jacobi matrices with spectral singularities, Math. Nachr., 229 (2001), 5–14.
E. Bairamov and A. O. C¸ elebi, Spectrum and spectral expansion for the non-selfadjoint discrete Dirae operators, Q. J. Math., Oxf. II. Ser., 50 (1999) 371–384.
E. Bairamov and C. Coskun, Jost solutions and the spectrum of the system of difference equations, Appl. Math. Lett., 17 (2004), 1039–1045.
M. G. Gasymov and B. M. Levitan, Determination of the Dirac system from scattering phase, Sov. Math., Dokl., 167 (1966), 1219–1222.
G. S. Guseinov, The inverse problem of scattering theory for a second order difference equation, Sov. Math., Dokl., 230 (1976), 1045–1048.
A. M. Krall, E. Bairamov and O. C¸ akar, ¨ Spectrum and spectral singularities of a quadratic pencil of a Schr¨odinger operator with a general boundry condition, J. Differ. Equations, 151 (1999), 252–267.
A. M. Krall, E. Bairamov and O. Cakar, Spectral analysis of non-selfadjoint discrete Sehr¨odinger operat¨ors with spectral singularities, Math. Nachr., 201 (2001), 89–104.
M. Jaulent and C. Jean, The inverse s-wave scattering problem for a class of potentials depending on energy, Commun. Math. Phys., 28 (1972), 177–220.
B. M. Levitan, Inverse Sturm-Liouville Problems, VSP, Zeist, (1987).
V. A. Marchenko, Sturm-Liouville Operators and Applications, Birkhauser Verlag, Basel, (1986).
