Direct and inverse spectral continuity for Dirac operators

Bessonov, Roman V. (author), Gubkin, Pavel (author)

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.

• Language: English
• Keywords: Dirac operators, Kronig-Penney model, Periodic spectral data, Schur algorithm, NLFT
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.04.2026
• Year: 2026
• Number of pages: Str. 351-411
• Numbering: Vol. 36, iss. 2
• PID: 20.500.12556/RUL-182504
• UDC: 517.9
• ISSN on article: 1016-443X
• DOI: 10.1007/s00039-026-00735-3
• COBISS.SI-ID: 278106627
• Publication date in RUL: 14.05.2026

Record is a part of a journal

• Title: Geometric and functional analysis
• Shortened title: Geom. funct. anal.
• Publisher: Springer International Publishing AG
• ISSN: 1016-443X
• COBISS.SI-ID: 512535577

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.