Dynamical and spectral Dirac systems: response function and inverse problems

Abstract

We establish simple connections between response functions of the dynamical Dirac systems and $A$-amplitudes and Weyl functions of the spectral Dirac systems. Using these connections we propose a new and rigorous procedure to recover a general-type dynamical Dirac system from its response function as well as a procedure to construct explicit solutions of this problem.

Some explanations (see p.3 and Remark 4.2) and several references are added in this version

References in corpus (4)

• Generalised Fourier transform for the Camassa-Holm hierarchy
• The boundary control approach to the Titchmarsh-Weyl $m-$function
• Inverse problem for one-dimensional dynamical Dirac system (BC-method)
• Inverse problem for Dirac systems with locally square-summable potentials and rectangular Weyl functions

Cited by in corpus (4)

• Dynamical canonical systems and their explicit solutions
• On a class of canonical systems corresponding to matrix string equations: general-type and explicit fundamental solutions and Weyl--Titchmarsh theory
• Continuous and discrete dynamical Schrödinger systems: explicit solutions
• Evolution of Weyl functions and initial-boundary value problems