What does this research mean for the field?

The spectral correspondence for half-line Dirac operators with L²-potentials is characterized by a two-sided uniform estimate, demonstrating continuity between close potentials and their spectral data. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This research aims to characterize half-line Dirac operators using spectral data and establish continuity relations.

March 12, 2026Open Access

Direct and Inverse Spectral Continuity for Dirac Operators

Key Points

This research aims to characterize half-line Dirac operators using spectral data and establish continuity relations.
Investigated half-line Dirac operators with L2-potentials.
Demonstrated a homeomorphic relation between close potentials and spectral data.
Provided explicit two-sided uniform estimates for spectral continuity.
Utilized Schur's algorithm to tackle the inverse spectral problem involving delta-interactions.
Established a clear uniform estimate for spectral continuity in the L2-case.
Confirmed the existence of a strong correspondence between potential configurations and spectral characteristics.

Abstract

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

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