Open Access

# Direct spectral problem for the generalized Jacobi Hermitian matrices

### Abstract

In this article we will introduce and investigate some generalized Jacobi matrices. These matrices have three-diagonal block structure and they are Hermitian. We will give necessary and sufficient conditions for selfadjointness of the operator which is generated by the matrix of such a type, and consider its generalized eigenvector expansion.

### Article Information

 Title Direct spectral problem for the generalized Jacobi Hermitian matrices Source Methods Funct. Anal. Topology, Vol. 15 (2009), no. 1, 3-14 MathSciNet MR2502634 Copyright The Author(s) 2009 (CC BY-SA)

### Authors Information

I. Ya. Ivasiuk
Kyiv National Taras Shevchenko University, Mechanics and Mathematics Faculty, Department of Mathematical Analysis, 64 Volodymyrs'ka, Kyiv, 01033, Ukraine

### Citation Example

I. Ya. Ivasiuk, Direct spectral problem for the generalized Jacobi Hermitian matrices, Methods Funct. Anal. Topology 15 (2009), no. 1, 3-14.

### BibTex

@article {MFAT474,
AUTHOR = {Ivasiuk, I. Ya.},
TITLE = {Direct spectral problem for the generalized Jacobi Hermitian matrices},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {15},
YEAR = {2009},
NUMBER = {1},
PAGES = {3-14},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=474},
}