A transfer matrix function representation of the fundamental solution of the general-type discrete Dirac system, corresponding to rectangular Schur coefficients and Weyl functions, is obtained. Connections with Szeg\"o recurrence, Schur coefficients and structured matrices are treated. Borg-Marchenko-type uniqueness theorem is derived. Inverse problems on the interval and semiaxis are solved.
@article{arxiv.1206.2915,
title = {Discrete Dirac system: rectangular Weyl functions, direct and inverse problems},
author = {B. Fritzsche and B. Kirstein and I. Roitberg and A. L. Sakhnovich},
journal= {arXiv preprint arXiv:1206.2915},
year = {2016}
}
Comments
Section 2 is improved in the second version: some new results on Halmos extension are added and arguments are simplified