To the Spectral Theory of One-Dimensional Matrix Dirac Operators with Point Matrix Interactions
- Authors: Budyka V.S.1, Malamud M.M.2, Posilicano A.3
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Affiliations:
- Donetsk Academy of Management and Public Administration
- Peoples’ Friendship University of Russia (RUDN University)
- Università dell’Insubria
- Issue: Vol 97, No 2 (2018)
- Pages: 115-121
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225471
- DOI: https://doi.org/10.1134/S1064562418020047
- ID: 225471
Cite item
Abstract
We 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.
About the authors
V. S. Budyka
Donetsk Academy of Management and Public Administration
Author for correspondence.
Email: budyka.vik@gmail.com
Ukraine, Donetsk
M. M. Malamud
Peoples’ Friendship University of Russia (RUDN University)
Email: budyka.vik@gmail.com
Russian Federation, Moscow, 117198
A. Posilicano
Università dell’Insubria
Email: budyka.vik@gmail.com
Italy, Como, 22100