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Centre de Recherches Mathematiques CRM Proceedings and Lecture Notes

Summary: Centre de Recherches Math´ematiques
CRM Proceedings and Lecture Notes
Volume 51, 2010
Two Variations on the Drury ­ Arveson Space
Nicola Arcozzi, Richard Rochberg, and Eric Sawyer
1. Introduction
The Drury ­ Arveson space DA is a Hilbert space of holomorphic functions on
Bn+1, the unit ball of Cn+1
. It was introduced by Drury [11] in 1978 in connec-
tion with the multivariable von Neumann inequality. Interest in the space grew
after an influential article by Arveson [7], and expanded further when Agler and
McCarthy [1] proved that DA is universal among the reproducing kernel Hilbert
spaces having the complete Nevanlinna ­ Pick property. The multiplier algebra of
DA plays an important role in these studies. Recently the authors obtained explicit
and rather sharp estimates for the norms of function acting as multipliers of DA
[3], an alternative proof is given in [17].
In our work we made use of a discretized version of the reproducing kernel for
DA, or, rather, of its real part. In this note we consider analogs of the DA space for
the Siegel domain, the unbounded generalized half-plane biholomorphically equiv-
alent to the ball. We also consider a discrete model of the of the Siegel domain


Source: Arcozzi, Nicola - Dipartimento di Matematica, Università di Bologna


Collections: Mathematics