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Dokl. Akad. Nauk, 2018, Volume 479, Number 2, Pages 117–125 (Mi dan47515)  

This article is cited in 2 scientific papers (total in 2 papers)

To the spectral theory of one-dimensional matrix Dirac operators with point matrix interactions

V. S. Budykaa, M. M. Malamudb, A. Posilicanoc

a Donetsk Academy of Management and Public Administration
b Peoples’ Friendship University of Russia (RUDN University)
c Università dell’Insubria

Abstract: AbstractWe investigate one-dimensional (2p × 2p)-matrix Dirac operators DX,α and DX,β with point matrix interactions on a discrete set X. Several results of [4] are generalized to the case of (p × p)-matrix interactions with p > 1. It is shown that a number of properties of the operators DX,α and DX,β (self-adjointness, discreteness of the spectrum, etc.) are identical to the corresponding properties of some Jacobi matrices BX,α and BX,β with (p × p)-matrix entries. The relationship found is used to describe these properties as well as conditions of continuity and absolute continuity of the spectra of the operators DX,α and DX,β. Also the non-relativistic limit at the velocity of light c → ∞ is studied.

DOI: https://doi.org/10.7868/S0869565218080017


English version:
Doklady Mathematics, 2018, 97:2, 115–121

Bibliographic databases:

UDC: 517.984

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. S. Budyka, M. M. Malamud, “On the Deficiency Indices of Block Jacobi Matrices Related to Dirac Operators with Point Interactions”, Math. Notes, 106:6 (2019), 1009–1014  mathnet  crossref  crossref  isi
    2. I. N. Braeutigam, D. M. Polyakov, “Asymptotics of eigenvalues of infinite block matrices”, Ufa Math. J., 11:3 (2019), 11–28  mathnet  crossref  isi
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