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Deficiency Indices of Block Jacobi Matrices: Survey

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Abstract

The paper is a survey and concerns with infinite symmetric block Jacobi matrices J with m × 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 J to have discrete spectrum.

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Authors and Affiliations

  1. Peoples Friendship University of Russia (RUDN University), Moscow, Russia

    V. Budyka & M. Malamud

  2. Donetsk Academy of Management and Public Administration, Donetsk, Ukraine

    V. Budyka

  3. Lomonosov Moscow State University, Moscow, Russia

    K. Mirzoev

  4. Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia

    K. Mirzoev

Authors
  1. V. Budyka
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  2. M. Malamud
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  3. K. Mirzoev
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Correspondence to V. Budyka.

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Dedicated to the memory of our friend, colleague, and blessed mathematician N. D. Kopachevsky.

Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 67, No. 2, Dedicated to the memory of Professor N. D. Kopachevsky, 2021.

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Budyka, V., Malamud, M. & Mirzoev, K. Deficiency Indices of Block Jacobi Matrices: Survey. J Math Sci 278, 39–54 (2024). https://doi.org/10.1007/s10958-024-06904-9

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