The H\"older continuity of spectral measures of an extended CMV matrix

TL;DR

This paper establishes the H"older continuity of spectral measures for extended CMV matrices, extending known results from discrete Schr"odinger operators to a unitary setting, based on solution bounds of the eigenvalue equation.

Contribution

It provides a unitary analogue of spectral measure regularity results previously known for discrete Schr"odinger operators, under power law bounds.

Findings

Spectral measures exhibit H"older continuity under certain conditions.

Results extend the understanding of spectral measures to unitary operators.

The approach parallels known results in the Schr"odinger operator context.

Abstract

We prove results about the H\"older continuity of the spectral measures of the extended CMV matrix, given power law bounds of the solution of the eigenvalue equation. We thus arrive at a unitary analogue of the results of Damanik, Killip and Lenz about the spectral measure of the discrete Schr\"odinger operator.