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Problem. Find a geometric characterization of the multipliers and of the Carleson measures for the infinite dimensional Drury-Arveson space.
 

Summary: Problem. Find a geometric characterization of the multipliers and of the Carleson
measures for the infinite dimensional Drury-Arveson space.
Discussion. The d-dimensional Drury-Arveson space is the closure of the complex
polynomials on the unit ball Bd of Cd
with respect to the norm
nNd
anzn
2
DAd
=
nNd
|an|2 n!
|n|!
.
Alternatively, DAd is the Hilbert function space having reproducing kernel K(z, w) =
(1 - z · w)-1
. The space DAd and its multiplier space M(DAd) were introduced by
Drury [3] in connection with the multivariable, commutative version of von Neu-
mann's inequality for contractions. The combinatorial, dimensionless nature of the
coefficients and the applications to Nevanlinna-Pick Theory [1] motivate the inter-

  

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

 

Collections: Mathematics