Wave operators for Jacobi matrices

TL;DR

This paper investigates the existence and completeness of wave operators for Jacobi matrices with spectral measures satisfying the Szeg"o condition, under mild assumptions on associated Verblunsky coefficients.

Contribution

It establishes conditions for the existence and completeness of wave operators for Jacobi matrices with spectral measures meeting the Szeg"o condition, extending previous results.

Findings

Proves existence of wave operators under Szeg"o condition

Demonstrates completeness of wave operators with mild assumptions

Links spectral measure properties to wave operator behavior

Abstract

We study the wave operators for a Jacobi matrix whose spectral measure satisfies the Szeg\"o condition. We prove existence and completeness of wave operators under a mild additional assumption on the Verblunsky coefficients of the associated measure on the unit circle.