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.

Full Text

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},
  MRNUMBER = {MR2502642},
       URL = {http://mfat.imath.kiev.ua/article/?id=484},
}