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

Autor:	Anton Kutsenko, Leonid Golinskii
Rok vydání:	2018
Předmět:	Pure mathematics Lebesgue measure 010102 general mathematics Spectrum (functional analysis) Block (permutation group theory) Order (ring theory) 01 natural sciences Upper and lower bounds Mathematics - Spectral Theory 47B36 47B39 35P15 Operator (computer programming) Mathematics - Classical Analysis and ODEs 0103 physical sciences Partial difference Direct integral Classical Analysis and ODEs (math.CA) FOS: Mathematics 010307 mathematical physics Geometry and Topology 0101 mathematics Spectral Theory (math.SP) Mathematical Physics Analysis Mathematics
DOI:	10.48550/arxiv.1809.07136
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::124deaee0fdb8799c5a476c73f912469 Zobrazit plný text záznamu