Open AccessDeficiency Indices of Block Jacobi Matrices: Survey
Author(s) -
В. С. Будыка,
M. M. Malamud,
Karahan A. Mirzoev
Publication year - 2021
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2021-67-2-237-254
Subject(s) - block (permutation group theory) , jacobi method , mathematics , matrix (chemical analysis) , pure mathematics , jacobi operator , spectrum (functional analysis) , algebra over a field , combinatorics , jacobi polynomials , orthogonal polynomials , chemistry , physics , quantum mechanics , chromatography
The paper is a survey and concerns with infinite symmetric block Jacobi matrices J with mm-matrix entries. We discuss several results on general block Jacobi matrices to be either self-adjoint or have maximal as well as intermediate deficiency indices. We also discuss several conditions for J to have discrete spectrum.