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# Inverse spectral problems for Jacobi matrix with finite perturbed parameters

### Abstract

For Jacobi matrices with finitely perturbed parameters, we get an explicit re\-presentation of the Weyl function, and solve inverse spectral problems, that is, we recover Jacobi matrices from spectral data. For the spectral data, we take the following: the spectral density of the absolutely continuous spectrum, with or without all the eigenvalues; the numerical parameters of the representation of one component of the vector-eigenfunction in terms of Chebyshev polynomials. We prove that these inverse problems have a unique solution, or only a finite number of solutions.

Key words: Jacobi matrix, direct and inverse spectral problems, generalized eigenvector, spectral function, m-function, Weyl solution.

### Article Information

 Title Inverse spectral problems for Jacobi matrix with finite perturbed parameters Source Methods Funct. Anal. Topology, Vol. 21 (2015), no. 3, 256-265 MathSciNet MR3521696 zbMATH 06630272 Milestones Received 28/04/2015 Copyright The Author(s) 2015 (CC BY-SA)

### Authors Information

L. P. Nizhnik
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine

### Citation Example

L. P. Nizhnik, Inverse spectral problems for Jacobi matrix with finite perturbed parameters, Methods Funct. Anal. Topology 21 (2015), no. 3, 256-265.

### BibTex

@article {MFAT836,
AUTHOR = {Nizhnik, L. P.},
TITLE = {Inverse spectral problems for Jacobi matrix with finite perturbed parameters},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {21},
YEAR = {2015},
NUMBER = {3},
PAGES = {256-265},
ISSN = {1029-3531},
MRNUMBER = {MR3521696},
ZBLNUMBER = {06630272},
URL = {http://mfat.imath.kiev.ua/article/?id=836},
}

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