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# Integral representations for spectral functions of some nonself-adjoint Jacobi matrices

### Abstract

We study a Jacobi matrix $J$ with complex numbers $a_n,\ n\in\mathbb Z_+,$ in the main diagonal such that $r_0 \leq {\rm Im}\, a_n \leq r_1,\ r_0,r_1\in\mathbb R$. We obtain an integral representation for the (generalized) spectral function of the matrix $J$. The method of our study is similar to Marchenko's method for nonself-adjoint differential operators.

### Article Information

 Title Integral representations for spectral functions of some nonself-adjoint Jacobi matrices Source Methods Funct. Anal. Topology, Vol. 15 (2009), no. 1, 91-100 MathSciNet MR2502642 Copyright The Author(s) 2009 (CC BY-SA)

### Authors Information

S. M. Zagorodnyuk
School of Mathematics and Mechanics, Karazin Kharkiv National University, 4 Svobody sq., Kharkiv, 61077, Ukraine

### Citation Example

S. M. Zagorodnyuk, Integral representations for spectral functions of some nonself-adjoint Jacobi matrices, Methods Funct. Anal. Topology 15 (2009), no. 1, 91-100.

### BibTex

@article {MFAT484,
AUTHOR = {Zagorodnyuk, S. M.},
TITLE = {Integral representations for spectral functions of some nonself-adjoint Jacobi matrices},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {15},
YEAR = {2009},
NUMBER = {1},
PAGES = {91-100},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=484},
}