Open AccessOn spectral properties of one class difference operators
Author(s) -
А. Г. Баскаков,
Галина Валериевна Гаркавенко,
M. Yu Glazkova,
Н. Б. Ускова
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1479/1/012002
Subject(s) - mathematics , diagonal , eigenvalues and eigenvectors , linear subspace , diagonal matrix , operator (biology) , operator theory , class (philosophy) , pure mathematics , matrix (chemical analysis) , invariant (physics) , main diagonal , algebra over a field , mathematical analysis , mathematical physics , physics , computer science , quantum mechanics , biochemistry , geometry , chemistry , materials science , repressor , artificial intelligence , transcription factor , composite material , gene
In this paper, we analyse basic facts of infinite matrix theory. We construct a similarity transform which allows one to represent matrices in a certain class of 5-th diagonal matrices of a difference operator in a diagonal or block-diagonal form. For such matrices, asymptotic estimates of eigenvalues and eigenvectors are obtained. Such matrices are considered in game theory. They are also used in the study fourth-order difference operators with growing potential. The problem of invariant subspaces is also considered.