Asymptotic phase, asymptotic modulus, and Titchmarsh-Weyl coefficient for a Dirac system

Abstract

This paper studies a series representation for the Jost function associated with a Dirac system. Under suitable hypotheses the series yields the asymptotic form of the Titchmarsh-Weyl coefficient, valid not only in sectors of the upper halfplane but also the real axis. The asymptotic form of the spectral function, higher derivatives of the Jost function, and the limiting form of the asymptotic phase are also considered. Extensions of certain scattering formulas known in the Schrödinger case are given for the Dirac system.