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

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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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
\Bibitem{Gus09} \by Gusein Sh.~Guseinov \paper Inverse Spectral Problems for Tridiagonal~$N$ by $N$~Complex Hamiltonians \jour SIGMA \yr 2009 \vol 5 \papernumber 018 \totalpages 28 \mathnet{http://mi.mathnet.ru/sigma364} \crossref{https://doi.org/10.3842/SIGMA.2009.018} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2481474} \zmath{https://zbmath.org/?q=an:1163.15012} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000267267900018} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78751642049} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
2. Guseinov G.Sh., “Construction of a Complex Jacobi Matrix from Two-Spectra”, Hacet J Math Stat, 40:2 (2011), 297–303
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
4. Guseinov G.Sh., “On an Inverse Problem for Two Spectra of Finite Jacobi Matrices”, Appl. Math. Comput., 218:14 (2012), 7573–7589
5. Guseinov G.Sh., “On Determination of a Finite Jacobi Matrix From Two Spectra”, CMES-Comp. Model. Eng. Sci., 84:5 (2012), 405–421
6. Guseinov G.Sh., “On a Discrete Inverse Problem for Two Spectra”, Discrete Dyn. Nat. Soc., 2012, 956407
7. Guseinov G.Sh., “A Class of Complex Solutions to the Finite Toda Lattice”, Math. Comput. Model., 57:5-6 (2013), 1190–1202
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
9. Guseinov, GS, “On construction of a complex finite Jacobi matrix from two spectra”, Electronic Journal of Linear Algebra, 26 (2013), 101–120
10. Guseinov, G.S., “Inverse spectral problems for complex Jacobi matrices”, Springer Proceedings in Mathematics and Statistics, 41, 2013, 149–163
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
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
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