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Advances in Applied Mathematics and Approximation Theory pp 149–163Cite as

Inverse Spectral Problems for Complex Jacobi Matrices

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 41))

Abstract

The paper deals with two versions of the inverse spectral problem for finite complex Jacobi matrices. The first is to reconstruct the matrix using the eigenvalues and normalizing numbers (spectral data) of the matrix. The second is to reconstruct the matrix using two sets of eigenvalues (two spectra), one for the original Jacobi matrix and one for the matrix obtained by deleting the last row and last column of the Jacobi matrix. Uuniqueness and existence results for solution of the inverse problems are established and an explicit procedure of reconstruction of the matrix from the spectral data is given. It is shown how the results can be used to solve finite Toda lattices subject to the complex-valued initial conditions.

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Authors and Affiliations

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

    Gusein Sh. Guseinov

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  1. Gusein Sh. Guseinov
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Correspondence to Gusein Sh. Guseinov .

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Editors and Affiliations

  1. , Department of Mathematical Sciences, The University of Memphis, Memphis, 38152, Tennessee, USA

    George A. Anastassiou

  2. , Department of Mathematics, TOBB Economics and Technology University, Sögütözü, Ankara, 06530, Turkey

    Oktay Duman

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Guseinov, G.S. (2013). Inverse Spectral Problems for Complex Jacobi Matrices. In: Anastassiou, G., Duman, O. (eds) Advances in Applied Mathematics and Approximation Theory. Springer Proceedings in Mathematics & Statistics, vol 41. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6393-1_9

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