On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications
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Publication:6306950
DOI10.3842/SIGMA.2019.050arXiv1809.07136WikidataQ127582935 ScholiaQ127582935MaRDI QIDQ6306950
Leonid B. Golinskii, Anton A. Kutsenko
Publication date: 19 September 2018
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.
Estimates of eigenvalues in context of PDEs (35P15) Linear difference operators (47B39) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)
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