Direct and Inverse Spectral Continuity for Dirac Operators

The half-line Dirac operators with L² L 2 -potentials can be characterized by their spectral data. It is known that the spectral correspondence is a homeomorphism: close potentials give rise to close spectral data and vice versa. We prove the first explicit two-sided uniform estimate related to this continuity in the general L² L 2 -case. The proof is based on an exact solution of the inverse spectral problem for Dirac operators with δ δ -interactions on a half-lattice in terms of the Schur’s algorithm for analytic functions.