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On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications
Symmetry, integrability and geometry: methods and applications, Tome 15 (2019) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {Leonid Golinskii and Anton Kutsenko},
     title = {On {Direct} {Integral} {Expansion} for {Periodic} {Block-Operator} {Jacobi} {Matrices} and {Applications}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a49/}
}
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Leonid Golinskii; Anton Kutsenko. On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications. Symmetry, integrability and geometry: methods and applications, Tome 15 (2019). http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a49/

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