Functional models and self-modeling property of minimal Dirac operators on the half-line

Abstract

We prove that minimal Dirac operators on the half-line are self-modeling, which means that such an operator is determined by its arbitrary unitary copy uniquely up to a transformation (shape equivalence) which changes its potential by a constant factor of modulus one. This result is obtained using the wave functional model of the minimal matrix Schr\"odinger operator on the half-line.