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

Yıl 2020, Cilt: 10 Sayı: 1, 226 - 239, 25.06.2020

Bayram Bala

https://doi.org/10.37094/adyujsci.594199

https://izlik.org/JA33AU99GG

Öz

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 c_M.  

Anahtar Kelimeler

Parseval formula , Spectral analysis , Two spectra

Kaynakça

• [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.