Stability for the inverse resonance problem for the CMV operator

TL;DR

This paper proves a stable method for reconstructing CMV operators from their resonances, showing that small changes in resonances lead to small changes in the operator coefficients, for operators with rapidly decaying coefficients.

Contribution

It provides a new proof and a stability result for the inverse resonance problem for CMV operators with super-exponentially decaying Verblunsky coefficients.

Findings

Reconstruction of CMV operators from resonances is stable.

Continuous dependence of operator coefficients on resonances is established.

New proof technique for the inverse resonance problem.

Abstract

For the class of unitary CMV operators with super-exponentially decaying Verblunsky coefficients we give a new proof of the inverse resonance problem of reconstructing the operator from its resonances - the zeros of the Jost function. We establish a stability result for the inverse resonance problem that shows continuous dependence of the operator coefficients on the location of the resonances.