Transfer-function realization for multipliers of the Arveson space

An interesting and recently much studied generalization of the classical Schur class is the class of contractive operator-valued multipliers for the reproducing kernel Hilbert space H(kd ) on the unit ball Bd ⊂ Cd , where kd is the positive kernel kd (λ, ζ ) = 1/(1 − λ, ζ ) on Bd . We study this space from the point of view of realization theory and functional models of de Branges–Rovnyak type.We highlight features which depart from the classical univariate case: coisometric realizations have only partial uniqueness properties, the nonuniqueness can be described explicitly, and this description assumes a particularly concrete form in the functional-model context. © 2006 Elsevier Inc. All rights reserved.