Spectral asymptotics for canonical systems

TL;DR

This paper introduces a novel approach to analyze the high-energy spectral behavior of canonical systems, improving classical results and addressing open problems, with applications to various differential operators.

Contribution

It develops a new method based on the continuity of the de Branges correspondence for studying spectral asymptotics of canonical systems.

Findings

Enhanced understanding of Weyl-Titchmarsh functions at high energies

Improved classical spectral asymptotics results

Applications to radial Dirac, Schrödinger operators, and strings

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 $2\times2$ 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 Schr\"odinger operators as well as to Krein strings and generalized indefinite strings.