Inverse spectral problems for Dirac operators with summable matrix-valued potentials

Abstract

We consider the direct and inverse spectral problems for Dirac operators on $(0,1)$ with matrix-valued potentials whose entries belong to $L_p(0,1)$, $p\in [1,\infty )$. We give a complete description of the spectral data (eigenvalues and suitably introduced norming matrices) for the operators under consideration and suggest a method for reconstructing the potential from the corresponding spectral data.

32 pages

References in corpus (3)

• Inverse spectral problems for Dirac operators with summable potentials
• Inverse spectral problems for Sturm--Liouville operators with matrix-valued potentials
• Inverse spectral problems for Dirac operators on a finite interval

Cited by in corpus (2)

• Singular Weyl-Titchmarsh-Kodaira theory for one-dimensional Dirac operators
• Canonical systems in ${\mathbb{R}}^2$ with periodic potentials and vanishing instability intervals