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

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.

Section 2 is improved in the second version: some new results on Halmos extension are added and arguments are simplified

References in corpus (2)

• Discrete skew selfadjoint canonical systems and the isotropic Heisenberg magnet model
• Weyl theory and explicit solutions of direct and inverse problems for a Dirac system with rectangular matrix potential

Cited by in corpus (6)

• Verblunsky-type coefficients for Dirac and canonical systems generated by Toeplitz and Hankel matrices, respectively
• Dressing for generalised linear Hamiltonian systems depending rationally on the spectral parameter and some applications
• Inverse problems for self-adjoint Dirac systems: explicit solutions and stability of the procedure
• Skew-selfadjoint Dirac systems with rational rectangular Weyl functions: explicit solutions of direct and inverse problems and integrable wave equations
• Discrete Dirac systems on the semiaxis: rational reflection coefficients and Weyl functions
• 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