Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians

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 nu...

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Main Author:	Gusein Sh. Guseinov
Format:	Article
Language:	English
Published:	National Academy of Science of Ukraine 2009-02-01
Series:	Symmetry, Integrability and Geometry: Methods and Applications
Subjects:	Jacobi matrix difference equation generalized spectral function spectral data
Online Access:	http://dx.doi.org/10.3842/SIGMA.2009.018

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spelling	doaj-dc7db0d53dc7429483c5400f7e7caff32020-11-25T00:53:51ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592009-02-015018Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians Gusein Sh. GuseinovIn 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.http://dx.doi.org/10.3842/SIGMA.2009.018Jacobi matrixdifference equationgeneralized spectral functionspectral data
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Gusein Sh. Guseinov
spellingShingle	Gusein Sh. Guseinov Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians Symmetry, Integrability and Geometry: Methods and Applications Jacobi matrix difference equation generalized spectral function spectral data
author_facet	Gusein Sh. Guseinov
author_sort	Gusein Sh. Guseinov
title	Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians
title_short	Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians
title_full	Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians
title_fullStr	Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians
title_full_unstemmed	Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians
title_sort	inverse spectral problems for tridiagonal n by n complex hamiltonians
publisher	National Academy of Science of Ukraine
series	Symmetry, Integrability and Geometry: Methods and Applications
issn	1815-0659
publishDate	2009-02-01
description	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.
topic	Jacobi matrix difference equation generalized spectral function spectral data
url	http://dx.doi.org/10.3842/SIGMA.2009.018
work_keys_str_mv	AT guseinshguseinov inversespectralproblemsfortridiagonalnbyncomplexhamiltonians
_version_	1725236277047984128

Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians

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