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Principal functions of non-selfadjoint matrix Sturm .Liouville operators with boundary conditions dependent on the spectral parameter

Year 2014, Volume: 63 Issue: 1, 25 - 34, 01.02.2014

Cafer Coskun Deniz Katar Murat Olgun

https://doi.org/10.1501/Commua1_0000000702

Keywords

Eigenvalues spectral singularities spectral analysis Sturm - Liouville

References

  • M. A. Naimark, Investigation of the spectrum and the expansion in eigenfunctions of a non- selfadjoint operators of second order on a semi-axis, AMS Translations 2(16) 1960, 103-193. [2] V. E. Lyance, A diğerential operator with spectral singularities, I, II, AMS Translations 2 (60)1967, 185-225, 227-283.
  • E. Bairamov, O. Cakar and A. O. Çelebi, Quadratic pencil of Schröndinger operators with spectral singularities: Discrete spectrum and principal functions, J. Math. Anal. Appl. 216 (1997), 303-320.
  • E. Bairamov, O. Cakar and A. M. Krall, Spectrum and spectral singularities of a quadratic pencil of a Schrödinger operator with a general boundary condition, J. Diğerential Equations 151 (1999), no. 2, 252–267.
  • E. Bairamov, O. Cakar and A. M. Krall, An eigenfunction expansion for a quadratic pencil of a Schrödinger operator with spectral singularities, J. Diğerential Equations 151 (1999), 268-289.
  • E. Bairamov and A. O. Celebi, Spectrum and spectral expansion for the non-selfadjoint discrete Dirac operators, Quart. J. Math. Oxford Ser. (2) 50 (1999), no. 200, 371–384.
  • E. Bairamov and A. O. Çelebi, Spectral properties of the Klein-Gordon s-wave equation with complex potential, Indian J. Pure Appl. Math. 28 (1997), 813-824.
  • E. Bairamov and G. B. Tunca, Discrete spectrum and principal functions of non-selfadjoint diğerential operators, Czechoslovak Math. J. 49 (1999), 689-700.
  • A. M. Krall, E. Bairamov and O. Cakar, Spectral analysis of a non-selfadjoint discrete Schrödinger operators with spectral singularities, Math. Nachr. 231 (2001), 89-104.
  • R. Carlson, An inverse problem for the matrix Schrödinger equation, J. Math. Anal. Appl. 267(2002), 564-575.
  • S. Clark and F. Gesztesy, Weyl-Titchmarsh M-function asymptotics, local uniqueness re- sults, trace formulas and Borg-type theorems for Dirac operators ,Trans Amer. Math. Soc. 354(2002), 3475-3534.
  • S. Clark, F. Gesztesy and W. Renger Trace formulas and Borg-type theorems for matrix- valued Jacobi and Dirac …nite diğerence operators, J. Diğerential Equations 219 (2005), 144-182.
  • F. Gesztesy, A. Kiselev and K. A. Makarov, Uniqueness results for matrix-valued Schrödinger, Jacobi and Dirac-type operators, Math. Nachr. 239 (2002), 103-145.
  • N. Yokus, Principal functions of non-selfadjoint Sturm-Liouville problems with eigenvalue- dependent boundary conditions,Abstract and Applied Analysis, (2011) 1-12.
  • M. Olgun, C. Coskun, Non-selfadjoint matrix Sturm-Liouville operators with spectral sin- gularities Applied Mathematics and Computations, 216 (8) (2010)
  • C. Coskun, M. Olgun, Principal functions of non-selfadjoint matrix Sturm-Liouville equations, Journal of Computational and Applied Mathematics, 235(2011).
  • Z. S. Agranovich, V. A. Marchenko, The Inverse Problem of Scattering Theory, Gordon and Breach, 1965.
  • E. Bairamov, and N. Yokus, Spectral Singularities of Sturm-Liouville Problems with Eigenvalue-Dependent Boundary Conditions, Abstract and Applied Analysis, 2009, 1-8.
  • M. Olgun, T. Koprubasi and Y. Aygar, Principal Functions of Non-Selfadjoint Diğerence Operator with Spectral Parameter in Boundary Conditions, Abstract and Applied Analysis, pp.1-11, 2011.
  • Y. Aygar, ;M. Olgun and T. Koprubasi, Principal Functions of Nonselfadjoint Discrete Dirac Equations with Spectral Parameter in Boundary Conditions,Abstract and Applied Analysis, pp.1-15,2012.
  • M. Olgun, Non-Selfadjoint Matrix Sturm-Liouville Operators with Eigenvalue-Dependent Boundary Conditions, Hacettepe J Math & Stat., (Accepted).
  • Current address : Ankara University, Faculty of Sciences
  • Department of Mathematics Ankara, TURKEY
  • E-mail address : ccoskun@ankara.edu.tr, deniz.ktr@hotmail.com, olgun@ankara.edu.tr
  • URL: http://communications.science.ankara.edu.tr/index.php?series=A1

Year 2014, Volume: 63 Issue: 1, 25 - 34, 01.02.2014

Cafer Coskun Deniz Katar Murat Olgun

https://doi.org/10.1501/Commua1_0000000702

References

  • M. A. Naimark, Investigation of the spectrum and the expansion in eigenfunctions of a non- selfadjoint operators of second order on a semi-axis, AMS Translations 2(16) 1960, 103-193. [2] V. E. Lyance, A diğerential operator with spectral singularities, I, II, AMS Translations 2 (60)1967, 185-225, 227-283.
  • E. Bairamov, O. Cakar and A. O. Çelebi, Quadratic pencil of Schröndinger operators with spectral singularities: Discrete spectrum and principal functions, J. Math. Anal. Appl. 216 (1997), 303-320.
  • E. Bairamov, O. Cakar and A. M. Krall, Spectrum and spectral singularities of a quadratic pencil of a Schrödinger operator with a general boundary condition, J. Diğerential Equations 151 (1999), no. 2, 252–267.
  • E. Bairamov, O. Cakar and A. M. Krall, An eigenfunction expansion for a quadratic pencil of a Schrödinger operator with spectral singularities, J. Diğerential Equations 151 (1999), 268-289.
  • E. Bairamov and A. O. Celebi, Spectrum and spectral expansion for the non-selfadjoint discrete Dirac operators, Quart. J. Math. Oxford Ser. (2) 50 (1999), no. 200, 371–384.
  • E. Bairamov and A. O. Çelebi, Spectral properties of the Klein-Gordon s-wave equation with complex potential, Indian J. Pure Appl. Math. 28 (1997), 813-824.
  • E. Bairamov and G. B. Tunca, Discrete spectrum and principal functions of non-selfadjoint diğerential operators, Czechoslovak Math. J. 49 (1999), 689-700.
  • A. M. Krall, E. Bairamov and O. Cakar, Spectral analysis of a non-selfadjoint discrete Schrödinger operators with spectral singularities, Math. Nachr. 231 (2001), 89-104.
  • R. Carlson, An inverse problem for the matrix Schrödinger equation, J. Math. Anal. Appl. 267(2002), 564-575.
  • S. Clark and F. Gesztesy, Weyl-Titchmarsh M-function asymptotics, local uniqueness re- sults, trace formulas and Borg-type theorems for Dirac operators ,Trans Amer. Math. Soc. 354(2002), 3475-3534.
  • S. Clark, F. Gesztesy and W. Renger Trace formulas and Borg-type theorems for matrix- valued Jacobi and Dirac …nite diğerence operators, J. Diğerential Equations 219 (2005), 144-182.
  • F. Gesztesy, A. Kiselev and K. A. Makarov, Uniqueness results for matrix-valued Schrödinger, Jacobi and Dirac-type operators, Math. Nachr. 239 (2002), 103-145.
  • N. Yokus, Principal functions of non-selfadjoint Sturm-Liouville problems with eigenvalue- dependent boundary conditions,Abstract and Applied Analysis, (2011) 1-12.
  • M. Olgun, C. Coskun, Non-selfadjoint matrix Sturm-Liouville operators with spectral sin- gularities Applied Mathematics and Computations, 216 (8) (2010)
  • C. Coskun, M. Olgun, Principal functions of non-selfadjoint matrix Sturm-Liouville equations, Journal of Computational and Applied Mathematics, 235(2011).
  • Z. S. Agranovich, V. A. Marchenko, The Inverse Problem of Scattering Theory, Gordon and Breach, 1965.
  • E. Bairamov, and N. Yokus, Spectral Singularities of Sturm-Liouville Problems with Eigenvalue-Dependent Boundary Conditions, Abstract and Applied Analysis, 2009, 1-8.
  • M. Olgun, T. Koprubasi and Y. Aygar, Principal Functions of Non-Selfadjoint Diğerence Operator with Spectral Parameter in Boundary Conditions, Abstract and Applied Analysis, pp.1-11, 2011.
  • Y. Aygar, ;M. Olgun and T. Koprubasi, Principal Functions of Nonselfadjoint Discrete Dirac Equations with Spectral Parameter in Boundary Conditions,Abstract and Applied Analysis, pp.1-15,2012.
  • M. Olgun, Non-Selfadjoint Matrix Sturm-Liouville Operators with Eigenvalue-Dependent Boundary Conditions, Hacettepe J Math & Stat., (Accepted).
  • Current address : Ankara University, Faculty of Sciences
  • Department of Mathematics Ankara, TURKEY
  • E-mail address : ccoskun@ankara.edu.tr, deniz.ktr@hotmail.com, olgun@ankara.edu.tr
  • URL: http://communications.science.ankara.edu.tr/index.php?series=A1
There are 24 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Cafer Coskun This is me

Deniz Katar This is me

Murat Olgun This is me

Publication Date February 1, 2014
Published in Issue Year 2014 Volume: 63 Issue: 1

Cite

APA Coskun, C., Katar, D., & Olgun, M. (2014). Principal functions of non-selfadjoint matrix Sturm .Liouville operators with boundary conditions dependent on the spectral parameter. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 63(1), 25-34. https://doi.org/10.1501/Commua1_0000000702
AMA Coskun C, Katar D, Olgun M. Principal functions of non-selfadjoint matrix Sturm .Liouville operators with boundary conditions dependent on the spectral parameter. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2014;63(1):25-34. doi:10.1501/Commua1_0000000702
Chicago Coskun, Cafer, Deniz Katar, and Murat Olgun. “Principal Functions of Non-Selfadjoint Matrix Sturm .Liouville Operators With Boundary Conditions Dependent on the Spectral Parameter”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 63, no. 1 (February 2014): 25-34. https://doi.org/10.1501/Commua1_0000000702.
EndNote Coskun C, Katar D, Olgun M (February 1, 2014) Principal functions of non-selfadjoint matrix Sturm .Liouville operators with boundary conditions dependent on the spectral parameter. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 63 1 25–34.
IEEE C. Coskun, D. Katar, and M. Olgun, “Principal functions of non-selfadjoint matrix Sturm .Liouville operators with boundary conditions dependent on the spectral parameter”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 63, no. 1, pp. 25–34, 2014, doi: 10.1501/Commua1_0000000702.
ISNAD Coskun, Cafer et al. “Principal Functions of Non-Selfadjoint Matrix Sturm .Liouville Operators With Boundary Conditions Dependent on the Spectral Parameter”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 63/1 (February 2014), 25-34. https://doi.org/10.1501/Commua1_0000000702.
JAMA Coskun C, Katar D, Olgun M. Principal functions of non-selfadjoint matrix Sturm .Liouville operators with boundary conditions dependent on the spectral parameter. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2014;63:25–34.
MLA Coskun, Cafer et al. “Principal Functions of Non-Selfadjoint Matrix Sturm .Liouville Operators With Boundary Conditions Dependent on the Spectral Parameter”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 63, no. 1, 2014, pp. 25-34, doi:10.1501/Commua1_0000000702.
Vancouver Coskun C, Katar D, Olgun M. Principal functions of non-selfadjoint matrix Sturm .Liouville operators with boundary conditions dependent on the spectral parameter. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2014;63(1):25-34.

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

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