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 CMFD, 2018, Volume 64, Issue 1, Pages 180–193 (Mi cmfd353)

Uniform basis property of the system of root vectors of the Dirac operator

A. M. Savchuk, I. V. Sadovnichaya

Lomonosov Moscow State University, Moscow, Russia

Abstract: We study one-dimensional Dirac operator $\mathcal L$ on the segment $[0,\pi]$ with regular in the sense of Birkhoff boundary conditions $U$ and complex-valued summable potential $P=(p_{ij}(x)),$ $i,j=1,2$. We prove uniform estimates for the Riesz constants of systems of root functions of a strongly regular operator $\mathcal L$ assuming that boundary-value conditions $U$ and the number $\int_0^\pi(p_1(x)-p_4(x)) dx$ are fixed and the potential $P$ takes values from the ball $B(0,R)$ of radius $R$ in the space $L_\varkappa$ for $\varkappa>1$. Moreover, we can choose the system of root functions so that it consists of eigenfunctions of the operator $\mathcal L$ except for a finite number of root vectors that can be uniformly estimated over the ball $\|P\|_\varkappa\le R$.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00706

DOI: https://doi.org/10.22363/2413-3639-2018-64-1-180-193

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UDC: 517.984.52

Citation: A. M. Savchuk, I. V. Sadovnichaya, “Uniform basis property of the system of root vectors of the Dirac operator”, Differential and functional differential equations, CMFD, 64, no. 1, Peoples' Friendship University of Russia, M., 2018, 180–193

Citation in format AMSBIB
\Bibitem{SavSad18} \by A.~M.~Savchuk, I.~V.~Sadovnichaya \paper Uniform basis property of the system of root vectors of the Dirac operator \inbook Differential and functional differential equations \serial CMFD \yr 2018 \vol 64 \issue 1 \pages 180--193 \publ Peoples' Friendship University of Russia \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd353} \crossref{https://doi.org/10.22363/2413-3639-2018-64-1-180-193} 

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This publication is cited in the following articles:
1. A. M. Savchuk, I. V. Sadovnichaya, “Spektralnyi analiz odnomernoi sistemy Diraka s summiruemym potentsialom i operatora Shturma—Liuvillya s koeffitsientami-raspredeleniyami”, Spektralnyi analiz, SMFN, 66, no. 3, Rossiiskii universitet druzhby narodov, M., 2020, 373–530
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