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

M. I. Belishev, S. A. Simonov

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 Schrödinger operator on the half-line.

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 Schrödinger operator on the half-line.

Paper Structure

This paper contains 4 sections, 7 theorems, 44 equations.

Table of Contents

  1. About the paper
  2. Minimal Dirac operators on the half-line
  3. Self-modeling property of minimal Schrödinger operators
  4. Self-modeling property of minimal Dirac operators

Key Result

Theorem 1

Minimal Dirac operators $D_{\rm min}(p)$ with potentials $p\in W^1_{\infty,\rm{loc}}(\mathbb R_+;\mathbb C)$ in the non-exceptional case are self-modeling. $\blacktriangleleft$$\blacktriangleleft$

Theorems & Definitions (14)

  • Definition 1
  • Definition 2
  • Theorem 1
  • Definition 3
  • Theorem 2
  • proof
  • Corollary 1
  • Theorem 3
  • Remark
  • Theorem 4
  • ...and 4 more