On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications
Spectral Theory
2019-07-03 v4 Classical Analysis and ODEs
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
Cite
@article{arxiv.1809.07136,
title = {On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications},
author = {Leonid Golinskii and Anton Kutsenko},
journal= {arXiv preprint arXiv:1809.07136},
year = {2019}
}