Szego condition, scattering, and vibration of Krein strings

TL;DR

This paper characterizes measures with finite logarithmic integral through dynamical methods, applying the results to Dirac operators and Krein strings within the framework of de Branges canonical systems.

Contribution

It introduces a dynamical characterization of measures with finite logarithmic integral and extends the analysis to Dirac operators and Krein strings using de Branges systems.

Findings

Dynamical characterization of measures with finite logarithmic integral

Application to Dirac operators and Krein strings

Extension of results within de Branges canonical systems

Abstract

We give a dynamical characterization of measures on the real line with finite logarithmic integral. The general case is considered in the setting of evolution groups generated by de Branges canonical systems. Obtained results are applied to the Dirac operators and Krein strings.