Deficiency indices of block Jacobi matrices: survey

V. Budyka ; M. Malamud ; K. Mirzoev

Contemporary Mathematics. Fundamental Directions, Dedicated to the memory of Professor N. D. Kopachevsky, Tome 67 (2021) no. 2, pp. 237-254.

Résumé

The paper is a survey and concerns with infinite symmetric block Jacobi matrices $\mathbf{J}$ with $m\times m$-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 $\mathbf{J}$ to have discrete spectrum.

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