TY - JOUR

T1 - Direct and Inverse Spectral Continuity for Dirac Operators

AU - Bessonov, RV

AU - Gubkin, PV

N1 - Times Cited in Web of Science Core Collection: 0 Total Times Cited: 0 Cited Reference Count: 67

PY - 2026/3/9

Y1 - 2026/3/9

N2 - The half-line Dirac operators with L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$L{2}$\end{document}-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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$L{2}$\end{document}-case. The proof is based on an exact solution of the inverse spectral problem for Dirac operators with delta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\delta $\end{document}-interactions on a half-lattice in terms of the Schur's algorithm for analytic functions.

AB - The half-line Dirac operators with L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$L{2}$\end{document}-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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$L{2}$\end{document}-case. The proof is based on an exact solution of the inverse spectral problem for Dirac operators with delta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\delta $\end{document}-interactions on a half-lattice in terms of the Schur's algorithm for analytic functions.

KW - Dirac operators

KW - Kronig-Penney model

KW - Periodic spectral data

KW - Schur's algorithm

KW - NLFT

KW - SCHRODINGER-OPERATORS

KW - JACOBI MATRICES

KW - SUM-RULES

KW - Schur’s algorithm

UR - https://www.mendeley.com/catalogue/8e949748-3534-3784-8240-d2f8b4a23f8b/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-105033370291&origin=inward

U2 - 10.1007/s00039-026-00735-3

DO - 10.1007/s00039-026-00735-3

M3 - статья

VL - 36

SP - 351

EP - 411

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

SN - 1016-443X

IS - 2

ER -