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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 018, 28 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.018 (Mi sigma364) 		 
This article is cited in 15 scientific papers (total in 15 papers)

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

Gusein Sh. Guseinov

Department of Mathematics, Atilim University, 06836 Incek, Ankara, Turkey
Full-text PDF (366 kB) Citations (15)
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DOI: https://doi.org/10.3842/SIGMA.2009.018
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.
Received: November 18, 2008; in final form February 9, 2009; Published online February 14, 2009
Bibliographic databases:
Document Type: Article
MSC: 15A29; 39A10
Language: English
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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    • This publication is cited in the following 15 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
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