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

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

2011-03-07

arxiv.org/abs/1103.1369v1

Mathematics

Functional Analysis

Scientific paper

We develop a $d$-variable analog of the two-component de Bran-ges-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)

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