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Year 2020, Volume: 10 Issue: 1, 226 - 239, 25.06.2020
https://doi.org/10.37094/adyujsci.594199

Abstract

References

  • [1] Hochstadt, H., On some inverse problems in matrix theory, Archiv der Mathematik, 18(2), 201-207, 1967.
  • [2] Hochstadt, H., On the construction of a Jacobi matrix from spectral data, Linear Algebra and Its Applications, 8(5), 435-446, 1974.
  • [3] Hochstadt, H., On the construction of a Jacobi matrix from mixed given data, Linear Algebra and its Applications, 28, 113-115, 1979.
  • [4] Fu, L., Hochstadt, H., Inverse theorems for Jacobi matrices, Journal of Mathematical Analysis and Applications, 47(1), 162-168, 1974.
  • [5] Gasymov, M.G., Guseinov, G.Sh., On inverse problems of spectral analysis for infinite Jacobi matrices in the limit-circle case, In Soviet Mathematics Doklady, 40, 627-630, 1990.
  • [6] Guseinov, G.Sh., Determination of an infinite non-selfadjoint Jacobi matrix from its generalized spectral function, Matematicheskie Zametki, 23, 237-248, 1978; English transl.: Mathematical Notes, 23, 130-136, 1978.
  • [7] Guseinov, G.Sh., The inverse problem from the generalized spectral matrix for a second order non-selfadjoint difference equation on the axis, Izvetsiya Akademii Nauk Azerb. SSR Ser. Fiz.-Tekhn. Mat. Nauk, 5, 16-22, 1978 (in Russian)
  • [8] Guseinov, G.Sh., An inverse spectral problem for complex Jacobi matrices, Communications in Nonlinear Science and Numerical Simulation, 15(4), 840-851, 2010.
  • [9] Guseinov, G.Sh., Construction of a complex Jacobi matrix from two-spectra, Hacettepe Journal of Mathematics and Statistics, 40(2), 2011.
  • [10] Guseinov, G. Sh., On construction of a complex finite Jacobi matrix from two-spectra, Electronic Journal of Linear Algebra, 26, 101-120, 2013.
  • [11] Guseinov, G.Sh., On a discrete inverse problem for two spectra, Discrete Dynamics in Nature and Society, 14 pages, 2012.
  • [12] Guseinov, G.Sh., On an inverse problem for two spectra of finite Jacobi matrices, Applied Mathematics and Computation, 218(14), 7573-7589, 2012.
  • [13] Guseinov, G.Sh., Inverse spectral problems for tridiagonal N by N complex hamiltonians, Symmetry Integrability and Geometry: Methods and Applications, 28 pages, 2009.
  • [14] Manafov, M.D., Bala, B., Inverse spectral problems for tridiagonal N by N complex hamiltonians with spectral parameter in the initial conditions, Adıyaman Üniversitesi Fen Bilimleri Dergisi, 3(1), 20-27, 2013.
  • [15] Akhmedova, E.N., Huseynov, H.M., On eigenvalues and eigenfunctions of one class of Sturm-Liouville operators with discontinuous coefficients, Transactions of National Academy of Sciences of Azerbaijan Series of Physical-Technical and Mathematical Sciences, 23-4, 7-18, 2003.
  • [16] Akhmedova, E.N., Huseynov, H.M., On inverse problem for Sturm-Liouville operators with discontinuous coefficients, Transactions of Saratov University, (Izv. Sarat. Univ.), 10(1), 3-9, 2010.
  • [17] Bala, B., Kablan, A., Manafov, M.Dzh., Direct and inverse spectral problems for discrete Sturm-Liouville problem with generalized function potential, Advances in Difference Equations, 2016(1), 172, 2016.
  • [18] Huseynov, H.M., Finite dimensional inverse problems, Transactions of National Academy of Sciences of Azerbaijan Series of Physical-Technical and Mathematical Sciences, 21(1), 80-87, 2001.
  • [19] Bala, B., Manafov, M.Dzh., Kablan, A., Inverse spectral problems for spectral data and two spectra of N by N tridiagonal almost-symmetric matrices, Applications and Applied Mathematics, 14(2), 12 pages, 2019.
  • [20] Manafov, M.Dzh., Kablan, A., Bala, B., Parseval equality of discrete Sturm-Liouville equation with periodic generalized function potentials, AIP Conference Proceedings. Vol. 1991. No. 1. AIP Publishing, 2018.
  • [21] Bas, E., Ozarslan, R., A new approach for higher-order difference equations and eigenvalue problems via physical potentials, The European Physical Journal Plus, 134(6), 253, 2019.

Inverse Spectral Problems for Second Order Difference Equations with Generalized Funtion Potentials by aid of Parseval Formula

Year 2020, Volume: 10 Issue: 1, 226 - 239, 25.06.2020
https://doi.org/10.37094/adyujsci.594199

Abstract

In the present study we are investigated inverse spectral problems for spectral
analysis and two spectra of matrix J by using equality
which is equivalance Parseval formula. The matrix J is NxN tridiagonal almost-symmetric
matrix. The mean of almost-symmetric is the entries above and below the main
diagonal are the same except the entries a
M and cM.  

References

  • [1] Hochstadt, H., On some inverse problems in matrix theory, Archiv der Mathematik, 18(2), 201-207, 1967.
  • [2] Hochstadt, H., On the construction of a Jacobi matrix from spectral data, Linear Algebra and Its Applications, 8(5), 435-446, 1974.
  • [3] Hochstadt, H., On the construction of a Jacobi matrix from mixed given data, Linear Algebra and its Applications, 28, 113-115, 1979.
  • [4] Fu, L., Hochstadt, H., Inverse theorems for Jacobi matrices, Journal of Mathematical Analysis and Applications, 47(1), 162-168, 1974.
  • [5] Gasymov, M.G., Guseinov, G.Sh., On inverse problems of spectral analysis for infinite Jacobi matrices in the limit-circle case, In Soviet Mathematics Doklady, 40, 627-630, 1990.
  • [6] Guseinov, G.Sh., Determination of an infinite non-selfadjoint Jacobi matrix from its generalized spectral function, Matematicheskie Zametki, 23, 237-248, 1978; English transl.: Mathematical Notes, 23, 130-136, 1978.
  • [7] Guseinov, G.Sh., The inverse problem from the generalized spectral matrix for a second order non-selfadjoint difference equation on the axis, Izvetsiya Akademii Nauk Azerb. SSR Ser. Fiz.-Tekhn. Mat. Nauk, 5, 16-22, 1978 (in Russian)
  • [8] Guseinov, G.Sh., An inverse spectral problem for complex Jacobi matrices, Communications in Nonlinear Science and Numerical Simulation, 15(4), 840-851, 2010.
  • [9] Guseinov, G.Sh., Construction of a complex Jacobi matrix from two-spectra, Hacettepe Journal of Mathematics and Statistics, 40(2), 2011.
  • [10] Guseinov, G. Sh., On construction of a complex finite Jacobi matrix from two-spectra, Electronic Journal of Linear Algebra, 26, 101-120, 2013.
  • [11] Guseinov, G.Sh., On a discrete inverse problem for two spectra, Discrete Dynamics in Nature and Society, 14 pages, 2012.
  • [12] Guseinov, G.Sh., On an inverse problem for two spectra of finite Jacobi matrices, Applied Mathematics and Computation, 218(14), 7573-7589, 2012.
  • [13] Guseinov, G.Sh., Inverse spectral problems for tridiagonal N by N complex hamiltonians, Symmetry Integrability and Geometry: Methods and Applications, 28 pages, 2009.
  • [14] Manafov, M.D., Bala, B., Inverse spectral problems for tridiagonal N by N complex hamiltonians with spectral parameter in the initial conditions, Adıyaman Üniversitesi Fen Bilimleri Dergisi, 3(1), 20-27, 2013.
  • [15] Akhmedova, E.N., Huseynov, H.M., On eigenvalues and eigenfunctions of one class of Sturm-Liouville operators with discontinuous coefficients, Transactions of National Academy of Sciences of Azerbaijan Series of Physical-Technical and Mathematical Sciences, 23-4, 7-18, 2003.
  • [16] Akhmedova, E.N., Huseynov, H.M., On inverse problem for Sturm-Liouville operators with discontinuous coefficients, Transactions of Saratov University, (Izv. Sarat. Univ.), 10(1), 3-9, 2010.
  • [17] Bala, B., Kablan, A., Manafov, M.Dzh., Direct and inverse spectral problems for discrete Sturm-Liouville problem with generalized function potential, Advances in Difference Equations, 2016(1), 172, 2016.
  • [18] Huseynov, H.M., Finite dimensional inverse problems, Transactions of National Academy of Sciences of Azerbaijan Series of Physical-Technical and Mathematical Sciences, 21(1), 80-87, 2001.
  • [19] Bala, B., Manafov, M.Dzh., Kablan, A., Inverse spectral problems for spectral data and two spectra of N by N tridiagonal almost-symmetric matrices, Applications and Applied Mathematics, 14(2), 12 pages, 2019.
  • [20] Manafov, M.Dzh., Kablan, A., Bala, B., Parseval equality of discrete Sturm-Liouville equation with periodic generalized function potentials, AIP Conference Proceedings. Vol. 1991. No. 1. AIP Publishing, 2018.
  • [21] Bas, E., Ozarslan, R., A new approach for higher-order difference equations and eigenvalue problems via physical potentials, The European Physical Journal Plus, 134(6), 253, 2019.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Bayram Bala 0000-0001-6515-6039

Publication Date June 25, 2020
Submission Date July 19, 2019
Acceptance Date March 3, 2020
Published in Issue Year 2020 Volume: 10 Issue: 1

Cite

APA Bala, B. (2020). Inverse Spectral Problems for Second Order Difference Equations with Generalized Funtion Potentials by aid of Parseval Formula. Adıyaman University Journal of Science, 10(1), 226-239. https://doi.org/10.37094/adyujsci.594199
AMA Bala B. Inverse Spectral Problems for Second Order Difference Equations with Generalized Funtion Potentials by aid of Parseval Formula. ADYU J SCI. June 2020;10(1):226-239. doi:10.37094/adyujsci.594199
Chicago Bala, Bayram. “Inverse Spectral Problems for Second Order Difference Equations With Generalized Funtion Potentials by Aid of Parseval Formula”. Adıyaman University Journal of Science 10, no. 1 (June 2020): 226-39. https://doi.org/10.37094/adyujsci.594199.
EndNote Bala B (June 1, 2020) Inverse Spectral Problems for Second Order Difference Equations with Generalized Funtion Potentials by aid of Parseval Formula. Adıyaman University Journal of Science 10 1 226–239.
IEEE B. Bala, “Inverse Spectral Problems for Second Order Difference Equations with Generalized Funtion Potentials by aid of Parseval Formula”, ADYU J SCI, vol. 10, no. 1, pp. 226–239, 2020, doi: 10.37094/adyujsci.594199.
ISNAD Bala, Bayram. “Inverse Spectral Problems for Second Order Difference Equations With Generalized Funtion Potentials by Aid of Parseval Formula”. Adıyaman University Journal of Science 10/1 (June 2020), 226-239. https://doi.org/10.37094/adyujsci.594199.
JAMA Bala B. Inverse Spectral Problems for Second Order Difference Equations with Generalized Funtion Potentials by aid of Parseval Formula. ADYU J SCI. 2020;10:226–239.
MLA Bala, Bayram. “Inverse Spectral Problems for Second Order Difference Equations With Generalized Funtion Potentials by Aid of Parseval Formula”. Adıyaman University Journal of Science, vol. 10, no. 1, 2020, pp. 226-39, doi:10.37094/adyujsci.594199.
Vancouver Bala B. Inverse Spectral Problems for Second Order Difference Equations with Generalized Funtion Potentials by aid of Parseval Formula. ADYU J SCI. 2020;10(1):226-39.

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