TY - JOUR T1 - Eigenvalues and scattering properties of difference operators with impulsive condition AU - Erdal, İbrahim AU - Yardımcı, Şeyhmus PY - 2019 DA - February Y2 - 2018 DO - 10.31801/cfsuasmas.459458 JF - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics JO - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. PB - Ankara University WT - DergiPark SN - 1303-5991 SP - 663 EP - 671 VL - 68 IS - 1 LA - en AB - In this work, we are concerned with difference operator of second order with impulsive condition. By the help of a transfer matrix M, we present scattering function of corresponding operator and examine the spectral properties of this impulsive problem. KW - Impulsive condition KW - difference operator KW - asymptotics KW - spectral singularities CR - Naimark, M. A., Investigation of the spectrum and the expansion in eigenfunctions of a non-selfadjoint operators of second order on a semi-axis, AMS Transl. (2), 16, (1960), 103-193. CR - Marchenko, V. A., Sturm-Liouville operators and applications, Birkhauser Verlag, Basel, 1986. CR - Agarwal, R. P., Difference equations and inequalities, in: Theory, Methods and Applications, Marcel Dekkar Inc., New York, Basel, 2000. CR - Kelley, W. G and Peterson, A. C., Difference equations: an introduction with applications, Harcourt Academic Press, 2001. CR - Akhiezer, N. I., The classical moment problem and some related questions in analysis, New York, 1965. CR - Bairamov, E. and Çelebi, A. O., Spectrum and spectral expansion for the non-selfadjoint discrete Dirac operators, Quart J. Math. Oxford, 50(2), (1999), 371-384. CR - Adıvar, M. and Bairamov, E., Spectral properties of non-selfadjoint difference operators, J. Math. Anal. Appl., 261, (2001), 461-478. CR - Bairamov, E., Çakar, Ö. and Krall, A. M., Non-selfadjoint difference operators and Jacobi matrices with spectral singularities, Math. Nachr, 229, 2001. CR - Adıvar, M. and Bairamov, E., Difference equations of second order with spectral singularities, J. Math. Anal. Appl., 277, (2003), 714-721. CR - Bairamov, E., Çakar, Ö. and Krall, A. M., An eigenfunction expansion for a quadratic pencil of a Schrödinger operator with spectral singularities, J. Differential Equations, 151, (1999), 268-289. CR - Bairamov, E. and Cebesoy, Ş., Spectral singularities of the matrix Schrödinger equations, Hacet J. Math. Stat., 45, (2016), 1007-1014. CR - Aygar, Y., Investigation of spectral analysis of matrix quantum difference equations with spectral singularities, Hacet. J. Math. Stat., 45, (2016), 999-1005. CR - Ugurlu, E and Bairamov, E., Dissipative operators with impulsive conditions, J. Math. Chem., 51(6), (2013), 1670-1680. CR - Mostafazadeh, A., Spectral singularities of a general point interaction, J. Phys. A. Math. Theory, 44, 375302, (2011), (9pp). CR - Allahverdiev, B. P., Bairamov, E. and Ugurlu, E., Eigenparameter dependent Sturm-Liouville problems in boundary conditions with transmission conditions , J. Math. Anal. Appl., 401(1), (2013), 388-396. CR - Bairamov, E., Aygar, Y. and Karslıoglu, D., Scattering analysis and spectrum of discrete Schrödinger equations with transmission conditions, Filomat, 31, 17, (2017), 5391--5399 CR - Guseinov, G. Sh., The inverse problem of scattering theory for a second order difference equation, Sov. Math., Dokl., 230, (1976), 1045-1048. CR - Berezanski, Y. M., Expansions in eigenfunctions of selfadjoint operators, AMS, Providence, 1968. CR - Naimark, M. A., Linear differential operators, Frederick Ungar Publishing Co. New York, 1968. UR - https://doi.org/10.31801/cfsuasmas.459458 L1 - https://dergipark.org.tr/en/download/article-file/534639 ER -