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SIGMA, 2009, Volume 5, 018, 28 pp. (Mi sigma364)  

This article is cited in 12 scientific papers (total in 12 papers)

Inverse Spectral Problems for Tridiagonal $N$ by $N$ Complex Hamiltonians

Gusein Sh. Guseinov

Department of Mathematics, Atilim University, 06836 Incek, Ankara, Turkey

Abstract: In this paper, the concept of generalized spectral function is introduced for finite-order tridiagonal symmetric matrices (Jacobi matrices) with complex entries. The structure of the generalized spectral function is described in terms of spectral data consisting of the eigenvalues and normalizing numbers of the matrix. The inverse problems from generalized spectral function as well as from spectral data are investigated. In this way, a procedure for construction of complex tridiagonal matrices having real eigenvalues is obtained.

Keywords: Jacobi matrix; difference equation; generalized spectral function; spectral data

DOI: https://doi.org/10.3842/SIGMA.2009.018

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Full text: http://emis.mi.ras.ru/.../018
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Bibliographic databases:

ArXiv: 0902.2464
MSC: 15A29; 39A10
Received: November 18, 2008; in final form February 9, 2009; Published online February 14, 2009
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Citation: Gusein Sh. Guseinov, “Inverse Spectral Problems for Tridiagonal $N$ by $N$ Complex Hamiltonians”, SIGMA, 5 (2009), 018, 28 pp.

Citation in format AMSBIB
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\by Gusein Sh.~Guseinov
\paper Inverse Spectral Problems for Tridiagonal~$N$ by $N$~Complex Hamiltonians
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\yr 2009
\vol 5
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Ergun E., Bairamov E., “On the eigenvalues of a 3 by 3 non-Hermitian Hamiltonian”, Journal of Mathematical Chemistry, 49:2 (2011), 609–617  crossref  mathscinet  zmath  isi  scopus
    2. Guseinov G.Sh., “Construction of a Complex Jacobi Matrix from Two-Spectra”, Hacet J Math Stat, 40:2 (2011), 297–303  mathscinet  zmath  isi
    3. Guseinov G.Sh., “An Inverse Problem for Two Spectra of Complex Finite Jacobi Matrices”, CMES-Comp. Model. Eng. Sci., 86:4 (2012), 301–319  mathscinet  isi
    4. Guseinov G.Sh., “On an Inverse Problem for Two Spectra of Finite Jacobi Matrices”, Appl. Math. Comput., 218:14 (2012), 7573–7589  crossref  mathscinet  zmath  isi  scopus
    5. Guseinov G.Sh., “On Determination of a Finite Jacobi Matrix From Two Spectra”, CMES-Comp. Model. Eng. Sci., 84:5 (2012), 405–421  mathscinet  isi
    6. Guseinov G.Sh., “On a Discrete Inverse Problem for Two Spectra”, Discrete Dyn. Nat. Soc., 2012, 956407  crossref  mathscinet  zmath  isi  scopus
    7. Guseinov G.Sh., “A Class of Complex Solutions to the Finite Toda Lattice”, Math. Comput. Model., 57:5-6 (2013), 1190–1202  crossref  mathscinet  isi  elib  scopus
    8. Huseynov A., Guseinov G.Sh., “Solution of the Finite Complex Toda Lattice by the Method of Inverse Spectral Problem”, Appl. Math. Comput., 219:10 (2013), 5550–5563  crossref  mathscinet  zmath  isi  elib  scopus
    9. Guseinov, GS, “On construction of a complex finite Jacobi matrix from two spectra”, Electronic Journal of Linear Algebra, 26 (2013), 101–120  crossref  mathscinet  zmath  isi
    10. Guseinov, G.S., “Inverse spectral problems for complex Jacobi matrices”, Springer Proceedings in Mathematics and Statistics, 41, 2013, 149–163  crossref  mathscinet  scopus
    11. Guseinov G.Sh., “on the Determination of a Complex Finite Jacobi Matrix From Spectral Data”, Univ. Politeh. Buchar. Sci. Bull.-Ser. A-Appl. Math. Phys., 77:4 (2015), 123–134  mathscinet  zmath  isi
    12. Bala B., Kablan A., Manafov M.D., “Direct and inverse spectral problems for discrete Sturm-Liouville problem with generalized function potential”, Adv. Differ. Equ., 2016, 172  crossref  mathscinet  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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