Direct and inverse spectral continuity for Dirac operators

Roman Bessonov; Pavel Gubkin

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arXiv · 2505.00485

Direct and inverse spectral continuity for Dirac operators

Roman Bessonov·Pavel Gubkin

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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.

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Roman Bessonov, Pavel Gubkin. 2025-05-01. Direct and inverse spectral continuity for Dirac operators. https://arxiv.org/abs/2505.00485

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