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Year 2020, , 157 - 160, 31.12.2020
https://doi.org/10.47000/tjmcs.822830

Abstract

References

  • Guseinov, G.Sh., {\em Determination of an infinite Jacobi matrix from scattering data}, Doklady Akademii Nauk SSSR, \textbf{227}(6)(1976), 1289--1292.
  • Guseinov, G.Sh., {\em The inverse problem of scattering theory for a second order difference equation on the whole axis}, Doklady Akademii Nauk SSSR, \textbf{17}(1976), 1684--1688.
  • Guseinov, G.Sh., {\em Determination of an infinite non-self-adjoint Jacobi matrix from its generalized spectral function}, Mathematical Notes, \textbf{23}(2)(1978), 130--136.
  • Guseinov, I.M., Khanmamedov, Ag. Kh., {\em The $t\rightarrow\infty$ asymptotic regime of the Cauchy problem solution for the Toda chain with threshold-type Initial data}, Theoretical and Mathematical Physics, \textbf{119}(1999), 739--749.
  • Khanmamedov, Ag. Kh., {\em Inverse scattering problem for a discrete Sturm-Liouville Operator on the entire line}, Doklady Akademii Nauk, \textbf{431}(1)(2010), 25--26.
  • Kishakevich, Yu.L., {\em Spectral function of Marchenko type for a difference operator of an even order}, Mathematical Notes, \textbf{11}(4)(1972), 266--271.
  • Marchenko, V.A., Sturm-Liouville Operators and Their Applications, Naukova Dumka, Kiev, 1977.
  • Zagorodnyuk, S., {\em The direct and inverse spectral problems for $\mathit{(2N+1)}$-diagonal complex transposition-antisymmetric matrices}, Methods Funct. Anal. Topology, \textbf{14}(2)(2008), 124--131.
  • Zagorodnyuk, S.M., {\em Direct and inverse spectral problems for $\mathit{(2N+1)}$-diagonal, complex, symmetric, non-Hermitian matrices}, Serdica Mathematical Journal, \textbf{30}(4)(2004), 471--482.

On The Solution of an Infinite System of Discrete Equations

Year 2020, , 157 - 160, 31.12.2020
https://doi.org/10.47000/tjmcs.822830

Abstract

 In this work, we construct the transformation operator for the infinite system of the difference equations 

$a_{n-2}y_{n-2}+b_{n-1}y_{n-1}+c_{n}y_{n}+b_{n}y_{n+1}+a_{n}y_{n+2}=\lambda y_{n}$ $(n=1,2,...)$,

where $a_{n}\neq0,$ $b_{n},$ $c_{n}$ $(n=1,2,3,...)$ are given complex numbers, investigate some important properties of the special solutions of the difference system.

References

  • Guseinov, G.Sh., {\em Determination of an infinite Jacobi matrix from scattering data}, Doklady Akademii Nauk SSSR, \textbf{227}(6)(1976), 1289--1292.
  • Guseinov, G.Sh., {\em The inverse problem of scattering theory for a second order difference equation on the whole axis}, Doklady Akademii Nauk SSSR, \textbf{17}(1976), 1684--1688.
  • Guseinov, G.Sh., {\em Determination of an infinite non-self-adjoint Jacobi matrix from its generalized spectral function}, Mathematical Notes, \textbf{23}(2)(1978), 130--136.
  • Guseinov, I.M., Khanmamedov, Ag. Kh., {\em The $t\rightarrow\infty$ asymptotic regime of the Cauchy problem solution for the Toda chain with threshold-type Initial data}, Theoretical and Mathematical Physics, \textbf{119}(1999), 739--749.
  • Khanmamedov, Ag. Kh., {\em Inverse scattering problem for a discrete Sturm-Liouville Operator on the entire line}, Doklady Akademii Nauk, \textbf{431}(1)(2010), 25--26.
  • Kishakevich, Yu.L., {\em Spectral function of Marchenko type for a difference operator of an even order}, Mathematical Notes, \textbf{11}(4)(1972), 266--271.
  • Marchenko, V.A., Sturm-Liouville Operators and Their Applications, Naukova Dumka, Kiev, 1977.
  • Zagorodnyuk, S., {\em The direct and inverse spectral problems for $\mathit{(2N+1)}$-diagonal complex transposition-antisymmetric matrices}, Methods Funct. Anal. Topology, \textbf{14}(2)(2008), 124--131.
  • Zagorodnyuk, S.M., {\em Direct and inverse spectral problems for $\mathit{(2N+1)}$-diagonal, complex, symmetric, non-Hermitian matrices}, Serdica Mathematical Journal, \textbf{30}(4)(2004), 471--482.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Anar Adiloğlu 0000-0001-5602-5272

Mehmet Gürdal 0000-0003-0866-1869

Publication Date December 31, 2020
Published in Issue Year 2020

Cite

APA Adiloğlu, A., & Gürdal, M. (2020). On The Solution of an Infinite System of Discrete Equations. Turkish Journal of Mathematics and Computer Science, 12(2), 157-160. https://doi.org/10.47000/tjmcs.822830
AMA Adiloğlu A, Gürdal M. On The Solution of an Infinite System of Discrete Equations. TJMCS. December 2020;12(2):157-160. doi:10.47000/tjmcs.822830
Chicago Adiloğlu, Anar, and Mehmet Gürdal. “On The Solution of an Infinite System of Discrete Equations”. Turkish Journal of Mathematics and Computer Science 12, no. 2 (December 2020): 157-60. https://doi.org/10.47000/tjmcs.822830.
EndNote Adiloğlu A, Gürdal M (December 1, 2020) On The Solution of an Infinite System of Discrete Equations. Turkish Journal of Mathematics and Computer Science 12 2 157–160.
IEEE A. Adiloğlu and M. Gürdal, “On The Solution of an Infinite System of Discrete Equations”, TJMCS, vol. 12, no. 2, pp. 157–160, 2020, doi: 10.47000/tjmcs.822830.
ISNAD Adiloğlu, Anar - Gürdal, Mehmet. “On The Solution of an Infinite System of Discrete Equations”. Turkish Journal of Mathematics and Computer Science 12/2 (December 2020), 157-160. https://doi.org/10.47000/tjmcs.822830.
JAMA Adiloğlu A, Gürdal M. On The Solution of an Infinite System of Discrete Equations. TJMCS. 2020;12:157–160.
MLA Adiloğlu, Anar and Mehmet Gürdal. “On The Solution of an Infinite System of Discrete Equations”. Turkish Journal of Mathematics and Computer Science, vol. 12, no. 2, 2020, pp. 157-60, doi:10.47000/tjmcs.822830.
Vancouver Adiloğlu A, Gürdal M. On The Solution of an Infinite System of Discrete Equations. TJMCS. 2020;12(2):157-60.