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Eigenvalues and scattering properties of difference operators with impulsive condition

Year 2019, Volume: 68 Issue: 1, 663 - 671, 01.02.2019
https://doi.org/10.31801/cfsuasmas.459458

Abstract

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.

References

  • 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.
  • Marchenko, V. A., Sturm-Liouville operators and applications, Birkhauser Verlag, Basel, 1986.
  • Agarwal, R. P., Difference equations and inequalities, in: Theory, Methods and Applications, Marcel Dekkar Inc., New York, Basel, 2000.
  • Kelley, W. G and Peterson, A. C., Difference equations: an introduction with applications, Harcourt Academic Press, 2001.
  • Akhiezer, N. I., The classical moment problem and some related questions in analysis, New York, 1965.
  • 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.
  • Adıvar, M. and Bairamov, E., Spectral properties of non-selfadjoint difference operators, J. Math. Anal. Appl., 261, (2001), 461-478.
  • Bairamov, E., Çakar, Ö. and Krall, A. M., Non-selfadjoint difference operators and Jacobi matrices with spectral singularities, Math. Nachr, 229, 2001.
  • Adıvar, M. and Bairamov, E., Difference equations of second order with spectral singularities, J. Math. Anal. Appl., 277, (2003), 714-721.
  • 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.
  • Bairamov, E. and Cebesoy, Ş., Spectral singularities of the matrix Schrödinger equations, Hacet J. Math. Stat., 45, (2016), 1007-1014.
  • Aygar, Y., Investigation of spectral analysis of matrix quantum difference equations with spectral singularities, Hacet. J. Math. Stat., 45, (2016), 999-1005.
  • Ugurlu, E and Bairamov, E., Dissipative operators with impulsive conditions, J. Math. Chem., 51(6), (2013), 1670-1680.
  • Mostafazadeh, A., Spectral singularities of a general point interaction, J. Phys. A. Math. Theory, 44, 375302, (2011), (9pp).
  • 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.
  • Bairamov, E., Aygar, Y. and Karslıoglu, D., Scattering analysis and spectrum of discrete Schrödinger equations with transmission conditions, Filomat, 31, 17, (2017), 5391--5399
  • Guseinov, G. Sh., The inverse problem of scattering theory for a second order difference equation, Sov. Math., Dokl., 230, (1976), 1045-1048.
  • Berezanski, Y. M., Expansions in eigenfunctions of selfadjoint operators, AMS, Providence, 1968.
  • Naimark, M. A., Linear differential operators, Frederick Ungar Publishing Co. New York, 1968.
Year 2019, Volume: 68 Issue: 1, 663 - 671, 01.02.2019
https://doi.org/10.31801/cfsuasmas.459458

Abstract

References

  • 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.
  • Marchenko, V. A., Sturm-Liouville operators and applications, Birkhauser Verlag, Basel, 1986.
  • Agarwal, R. P., Difference equations and inequalities, in: Theory, Methods and Applications, Marcel Dekkar Inc., New York, Basel, 2000.
  • Kelley, W. G and Peterson, A. C., Difference equations: an introduction with applications, Harcourt Academic Press, 2001.
  • Akhiezer, N. I., The classical moment problem and some related questions in analysis, New York, 1965.
  • 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.
  • Adıvar, M. and Bairamov, E., Spectral properties of non-selfadjoint difference operators, J. Math. Anal. Appl., 261, (2001), 461-478.
  • Bairamov, E., Çakar, Ö. and Krall, A. M., Non-selfadjoint difference operators and Jacobi matrices with spectral singularities, Math. Nachr, 229, 2001.
  • Adıvar, M. and Bairamov, E., Difference equations of second order with spectral singularities, J. Math. Anal. Appl., 277, (2003), 714-721.
  • 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.
  • Bairamov, E. and Cebesoy, Ş., Spectral singularities of the matrix Schrödinger equations, Hacet J. Math. Stat., 45, (2016), 1007-1014.
  • Aygar, Y., Investigation of spectral analysis of matrix quantum difference equations with spectral singularities, Hacet. J. Math. Stat., 45, (2016), 999-1005.
  • Ugurlu, E and Bairamov, E., Dissipative operators with impulsive conditions, J. Math. Chem., 51(6), (2013), 1670-1680.
  • Mostafazadeh, A., Spectral singularities of a general point interaction, J. Phys. A. Math. Theory, 44, 375302, (2011), (9pp).
  • 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.
  • Bairamov, E., Aygar, Y. and Karslıoglu, D., Scattering analysis and spectrum of discrete Schrödinger equations with transmission conditions, Filomat, 31, 17, (2017), 5391--5399
  • Guseinov, G. Sh., The inverse problem of scattering theory for a second order difference equation, Sov. Math., Dokl., 230, (1976), 1045-1048.
  • Berezanski, Y. M., Expansions in eigenfunctions of selfadjoint operators, AMS, Providence, 1968.
  • Naimark, M. A., Linear differential operators, Frederick Ungar Publishing Co. New York, 1968.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Review Articles
Authors

İbrahim Erdal 0000-0002-4445-2389

Şeyhmus Yardımcı 0000-0002-1062-9000

Publication Date February 1, 2019
Submission Date January 11, 2018
Acceptance Date May 8, 2018
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

APA Erdal, İ., & Yardımcı, Ş. (2019). Eigenvalues and scattering properties of difference operators with impulsive condition. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 663-671. https://doi.org/10.31801/cfsuasmas.459458
AMA Erdal İ, Yardımcı Ş. Eigenvalues and scattering properties of difference operators with impulsive condition. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):663-671. doi:10.31801/cfsuasmas.459458
Chicago Erdal, İbrahim, and Şeyhmus Yardımcı. “Eigenvalues and Scattering Properties of Difference Operators With Impulsive Condition”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 663-71. https://doi.org/10.31801/cfsuasmas.459458.
EndNote Erdal İ, Yardımcı Ş (February 1, 2019) Eigenvalues and scattering properties of difference operators with impulsive condition. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 663–671.
IEEE İ. Erdal and Ş. Yardımcı, “Eigenvalues and scattering properties of difference operators with impulsive condition”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 663–671, 2019, doi: 10.31801/cfsuasmas.459458.
ISNAD Erdal, İbrahim - Yardımcı, Şeyhmus. “Eigenvalues and Scattering Properties of Difference Operators With Impulsive Condition”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 663-671. https://doi.org/10.31801/cfsuasmas.459458.
JAMA Erdal İ, Yardımcı Ş. Eigenvalues and scattering properties of difference operators with impulsive condition. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:663–671.
MLA Erdal, İbrahim and Şeyhmus Yardımcı. “Eigenvalues and Scattering Properties of Difference Operators With Impulsive Condition”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 663-71, doi:10.31801/cfsuasmas.459458.
Vancouver Erdal İ, Yardımcı Ş. Eigenvalues and scattering properties of difference operators with impulsive condition. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):663-71.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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