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arXiv · 1809.07136

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

Leonid Golinskii·Anton Kutsenko
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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.

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Leonid Golinskii, Anton Kutsenko. 2018-09-19. On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications. https://doi.org/10.3842/sigma.2019.050

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