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

TL;DR

This paper demonstrates that minimal Dirac operators on the half-line are uniquely determined by their unitary copies up to a shape-preserving transformation, using wave functional models.

Contribution

It establishes the self-modeling property of minimal Dirac operators on the half-line, linking their structure to wave functional models of Schrödinger operators.

Findings

Minimal Dirac operators are self-modeling.

Operators are uniquely determined by their unitary copies.

Potential changes by a constant phase factor under transformations.

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.