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On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications (1809.07136v4)
Published 19 Sep 2018 in math.SP and math.CA
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.