Properties of root vector functions for the one-dimensional Dirac operator
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.
scientific article; zbMATH DE number 5809137