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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2019
• ISSN: 1815-0659
• Main Authors: Golinskii, L., Kutsenko, A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2019
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210172
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On Direct Integral Expansion for Periodic Block-Operator Jacobi Matrices and Applications / L. Golinskii, A. Kutsenko // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 12 назв. — англ.

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 spectr...