Properties of root vector functions for the one-dimensional Dirac operator
type: Item
instance of: scholarly article
title: Properties of root vector functions for the one-dimensional Dirac operator
zbMATH Open document ID: 1204.47053
DOI: 10.1134/S1064562410040307
author: V. M. Kurbanov
author: A. I. Ismailova
published in: Doklady Mathematics
publication date: 2010-11-01T00:00:00Z
review text: The authors consider the one-dimensional Dirac operator \[ Du= B {{du}\over {dx}}+P(x)u,\quad u=(u^1,u^2)^{T}, \] defined on an arbitrary interval \((a,b)\), where \(B=(b_{ij})^2_{i,j=1},\) \(b_{i,3-i}=(-1)^{i-1},\) \(b_{ii}=0,\) and \(P(x)=(_{ij}(x))^2_{i,j=1}\) is a complex-valued matrix function. The properties of the root vector functions of this operator are studied. Precisely, the authors obtain a priori estimates, estimates between various \(L^p\) norms of the root vector functions, and a criterion for the Riesz property for the systems of root vector functions. Moreover, results on componentwise equiconvergence which is uniform over compact sets and a componentwise localization principle are given.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 5809137
zbMATH Keywords: Dirac operator
zbMATH Keywords: root vector functions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5809137