Spectral asymptotics for canonical systems

Abstract

Based on continuity properties of the de Branges correspondence, we develop a new approach to study the high-energy behavior of Weyl-Titchmarsh and spectral functions of $2\times 2$ first order canonical systems. Our results improve several classical results and solve open problems posed by previous authors. Furthermore, they are applied to radial Dirac and radial Schrödinger operators as well as to Krein strings and generalized indefinite strings.

28 pages

References in corpus (8)

• Weyl-Titchmarsh Theory for Sturm-Liouville Operators with Distributional Potentials
• On the Singular Weyl-Titchmarsh Function of Perturbed Spherical Schroedinger Operators
• An isospectral problem for global conservative multi-peakon solutions of the Camassa-Holm equation
• Canonical systems and de Branges spaces
• The similarity problem for $J$-nonnegative Sturm-Liouville operators
• The inverse spectral problem for indefinite strings
• Quadratic operator pencils associated with the conservative Camassa-Holm flow
• On Spectral Deformations and Singular Weyl Functions for One-Dimensional Dirac Operators

Cited by in corpus (18)

• The inverse spectral problem for indefinite strings
• Dispersion Estimates for One-Dimensional Schrödinger Equations with Singular Potentials
• On Spectral Deformations and Singular Weyl Functions for One-Dimensional Dirac Operators
• Zero Measure and Singular Continuous Spectra for Quantum Graphs
• Unique solvability of a coupling problem for entire functions
• Reflectionless canonical systems, I. Arov gauge and right limits
• On a class of canonical systems corresponding to matrix string equations: general-type and explicit fundamental solutions and Weyl--Titchmarsh theory
• Reflectionless canonical systems, II. Almost periodicity and character-automorphic Fourier transforms
• Trace formulas and inverse spectral theory for generalized indefinite strings
• Continued fraction expansions of Herglotz-Nevanlinna functions and generalized indefinite strings of Stieltjes type
• On quasi-Herglotz functions in one variable
• An approach to universality using Weyl m-functions
• On the solution of the inverse problem for a class of canonical systems corresponding to matrix string equations
• Generalised canonical systems related to matrix string equations: corresponding structured operators and high-energy asymptotics of the Weyl functions
• Canonical systems whose Weyl coefficients have dominating real part
• The conservative Camassa-Holm flow with step-like irregular initial data
• Jacobi matrices with lacunary spectrum
• Limit behaviour of Weyl coefficients