Open AccessUniform Basis Property of the System of Root Vectors of the Dirac Operator
Author(s) -
А. М. Савчук,
I. V. Sadovnichaya
Publication year - 2018
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2018-64-1-180-193
Subject(s) - mathematics , eigenfunction , ball (mathematics) , dirac operator , boundary value problem , mathematical analysis , operator (biology) , pure mathematics , mathematical physics , eigenvalues and eigenvectors , physics , quantum mechanics , biochemistry , chemistry , repressor , transcription factor , gene
We study one-dimensional Dirac operator L on the segment [0,π] with regular in the sense of Birkhoff boundary conditions U and complex-valued summable potential P=(pij(x)), i,j=1,2. We prove uniform estimates for the Riesz constants of systems of root functions of a strongly regular operator L assuming that boundary-value conditions U and the number ∫(p1(x)-p4(x))dx are fixed and the potential P takes values from the ball B(0,R) of radius R in the space Lϰ for ϰ>1. Moreover, we can choose the system of root functions so that it consists of eigenfunctions of the operator L except for a finite number of root vectors that can be uniformly estimated over the ball ∥P∥ϰ≤R.