Discrete Dirac system: rectangular Weyl functions, direct and inverse problems

2012/06/30 by B. Fritzsche, B. Kirstein, I. Roitberg +1 · 1 citation
Mathematics · #math.CA #math.SP #msc:34B20 #msc:34L40 #msc:39A12 #msc:47A57

paper · pdf · doi:10.7153/oam-08-45

published as Oper. Matrices 8 (2014), 799-819 · Section 2 is improved in the second version: some new results on Halmos extension are added and arguments are simplified

arxiv created 2012/11/28 · arxiv updated 2016/11/03

Abstract

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 Szegö recurrence, Schur coefficients and structured matrices are treated. Borg-Marchenko-type uniqueness theorem is derived. Inverse problems on the interval and semiaxis are solved.

Cited by

• General-type discrete self-adjoint Dirac systems: explicit solutions of direct and inverse problems, asymptotics of Verblunsky-type coefficients and stability of solving inverse problem

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