Direct and inverse spectral continuity for Dirac operators

2025/05/01 by Bessonov, Roman, Gubkin, Pavel
#34L40 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2505.00485

Abstract

The half-line Dirac operators with L²-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-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.

Citations

• Stability of Schur's iterates and fast solution of the discrete integrable NLS
• Etudes for the inverse spectral problem
• An approach to universality using Weyl m-functions
• Pointwise convergence of the non-linear Fourier transform
• Szegő's Theorem for Canonical Systems: the Arov Gauge and a Sum Rule
• Killip-Simon problem and Jacobi flow on GMP matrices
• Canonical systems and de Branges spaces
• Spectral analysis of the half-line Kronig-Penney model with Wigner-von Neumann perturbations
• Analyticity and uniform stability of the inverse singular Sturm--Liouville spectral problem
• Continuous analogs of polynomials orthogonal on the unit circle. Krein systems
• Sum rules and spectral measures of Schrodinger operators with L² potentials
• The inverse Sturm-Liouville problem with mixed boundary conditions
• Orthogonal polynomials with exponentially decaying recursion coefficients
• On Extensions of a Theorem of Baxter
• Sum Rules for Jacobi Matrices and Their Applications to Spectral Theory
• On the Inverse Scattering Problem for Jacobi Matrices¶with the Spectrum on an Interval, a Finite System¶of Intervals or a Cantor Set of Positive Length

Related

• Inverse problems for Dirac operators with a constant delay less than half of the interval
• Inverse Problems For Dirac Operators With a Finite Number of Transmission Conditions
• Spectral Theory of Dirac Operators
• Direct spectral problem for a Dirac operator with non-local potential
• Spectral theory of boundary value problems for Dirac type operators