On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications
Leonid Borisovich Golinskii, Anton A. Kutsenko · Symmetry Integrability and Geometry Methods and Applications · 2019
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.