Inverse spectral problems for 2m-dimensional canonical Dirac operators

The inverse spectral problems for 2m-dimensional canonical Dirac operators with continuously differentiable self-adjoint 2m × 2m matrix potential are studied. The paper proves that if the spectrum is the same as the spectrum belonging to the zero potential, under some special boundary conditions, then the potential is actually zero. The proof is based on the fact that the squares of eigenvalues for Dirac operators are eigenvalues for corresponding vectorial Sturm–Liouville operators, which are the second power of 2m-dimensional Dirac operators.