Direct and inverse spectral continuity for Dirac operators

TL;DR

This paper establishes explicit two-sided uniform estimates demonstrating the spectral continuity of Dirac operators with $L^2$-potentials, using inverse spectral problem solutions and Schur's algorithm.

Contribution

It provides the first explicit two-sided uniform estimate for spectral continuity of Dirac operators with $L^2$-potentials.

Findings

Established explicit uniform estimates for spectral continuity.

Connected spectral data with $L^2$-potentials via inverse spectral problem.

Applied Schur's algorithm to Dirac operators with $oldsymbol{ ext{delta}}$-interactions.

Abstract

The half-line Dirac operators with $L^2$-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 $L^2$-case. The proof is based on an exact solution of the inverse spectral problem for Dirac operators with $\delta$-interactions on a half-lattice in terms of the Schur's algorithm for analytic functions.