Properties of Root Vector Functions for the One-Dimensional Dirac Operator

Properties of root vector functions for the one-dimensional Dirac operator are discussed. Additionally, theorems on component wise equiconvergence that is uniform on a compact set and a component wise localization principle are proved. Various equations have been provided in support of the problem. The system also contains the corresponding eigenfunction and all the associated vector functions of orders less than k. Component wise equiconvergence and the component wise localization principle for the Schr̈odinger operator with a matrix potential has been established. The proofs of all the theorems on component wise equiconvergence are based on the mean value formula.