article

Title: Canonical transfer-function realization for Schur multipliers on the Drury-Arveson space and models for commuting row contractions

Authors: Vladimir Bolotnikov and Joseph A. Ball

Issue: Volume 61 (2012), Issue 2, 665-716

Abstract:

We develop a $d$-variable analog of the two-component de Branges-Rovnyak reproducing kernel Hilbert space associated with a Schur-class function on the unit disk. In this generalization, the unit disk is replaced by the unit ball in $d$-dimensional complex Euclidean space, and the Schur class becomes the class of contractive multipliers on the Drury-Arveson space over the ball. We also develop some results on a model theory for commutative row contractions which are not necessarily completely noncoisometric (the case considered in earlier work of Bhattacharyya, Eschmeier, and Sarkar).