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Symmetry, Integrability and Geometry: Methods and Applications, 2019, Volume 15, 050, 14 pp.
DOI: https://doi.org/10.3842/SIGMA.2019.050
(Mi sigma1486)
 

On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications

Leonid Golinskiia, Anton Kutsenkob

a B. Verkin Institute for Low Temperature Physics and Engineering, 47 Science Ave., Kharkiv 61103, Ukraine
b Jacobs University, Campus Ring 1, 28759 Bremen, Germany
References:
Abstract: We construct a functional model (direct integral expansion) and study the spectra of certain periodic block-operator Jacobi matrices, in particular, of general 2D partial difference operators of the second order. We obtain the upper bound, optimal in a sense, for the Lebesgue measure of their spectra. The examples of the operators for which there are several gaps in the spectrum are given.
Keywords: functional model, block Jacobi matrices, partial difference operators, periodicity, spectrum.
Received: December 3, 2018; in final form June 23, 2019; Published online July 2, 2019
Bibliographic databases:
Document Type: Article
MSC: 47B36, 47B39, 35P15
Language: English
Citation: Leonid Golinskii, Anton Kutsenko, “On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications”, SIGMA, 15 (2019), 050, 14 pp.
Citation in format AMSBIB
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\paper On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications
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