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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
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
Citation:
Leonid Golinskii, Anton Kutsenko, “On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications”, SIGMA, 15 (2019), 050, 14 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1486 https://www.mathnet.ru/eng/sigma/v15/p50
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Statistics & downloads: |
Abstract page: | 161 | Full-text PDF : | 31 | References: | 20 |
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