
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 onedimensional matrix Dirac operators with point matrix interactions
V. S. Budyka^{a}, M. M. Malamud^{b}, A. Posilicano^{c} ^{a} Donetsk Academy of Management and Public Administration
^{b} PeoplesÃ¢Â€Â™ Friendship University of Russia (RUDN University)
^{c} UniversitÃƒÂ dellÃ¢Â€Â™Insubria
Abstract:
AbstractWe investigate onedimensional (2p ÃƒÂ— 2p)matrix Dirac operators DX,ÃŽÂ± and DX,ÃŽÂ² with point matrix interactions on a discrete set X. Several results of [4] are generalized to the case of (p ÃƒÂ— p)matrix interactions with p > 1. It is shown that a number of properties of the operators DX,ÃŽÂ± and DX,ÃŽÂ² (selfadjointness, discreteness of the spectrum, etc.) are identical to the corresponding properties of some Jacobi matrices BX,ÃŽÂ± and BX,ÃŽÂ² with (p ÃƒÂ— 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,ÃŽÂ± and DX,ÃŽÂ². Also the nonrelativistic limit at the velocity of light c Ã¢Â†Â’ Ã¢ÂˆÂž 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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http://mi.mathnet.ru/eng/dan47515
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This publication is cited in the following articles:

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

I. N. Braeutigam, D. M. Polyakov, “Asymptotics of eigenvalues of infinite block matrices”, Ufa Math. J., 11:3 (2019), 11–28

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