Description of Helson-Szeg\"o measures in terms of the Schur parameter sequences of associated Schur functions

TL;DR

This paper characterizes Helson-Szeg"o measures on the unit circle using the Schur parameters of associated Schur functions, providing a new perspective on their structure and properties.

Contribution

It introduces a novel characterization of Helson-Szeg"o measures through the analysis of Schur parameter sequences of related Schur functions.

Findings

Characterization of Helson-Szeg"o measures via Schur parameters

Link between measure properties and Schur function parameters

New criteria for identifying Helson-Szeg"o measures

Abstract

Let mu be a probability measure on the Borelian sigma-algebra of the unit circle. Then we associate a Schur function theta in the unit disk with mu and give characterizations of the case that mu is a Helson-Szeg\"o measure in terms of the sequence of Schur parameters of theta.