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1. CMB 2008 (vol 51 pp. 481)
Universal Inner Functions on the Ball It is shown that given any sequence of automorphisms $(\phi_k)_k$ of the
unit ball $\bn$ of $\cn$ such that $\|\phi_k(0)\|$ tends to $1$,
there exists an inner function
$I$ such that the family of ``non-Euclidean translates"
$(I\circ\phi_k)_k$ is locally uniformly dense in the unit ball of
$H^\infty(\bn)$.
Keywords:inner functions, automorphisms of the ball, universality Categories:32A35, 30D50, 47B38 |
2. CMB 2006 (vol 49 pp. 381)
On the Membership in Bergman Spaces of the Derivative of a Blaschke Product With Zeros in a Stolz Domain |
On the Membership in Bergman Spaces of the Derivative of a Blaschke Product With Zeros in a Stolz Domain It is known that the derivative of
a Blaschke product whose zero sequence lies in a Stolz angle
belongs to all the Bergman spaces $A^p$ with $0
1$). As a consequence, we prove that there exists a Blaschke product $B$ with zeros on a radius such that $B'\notin A^{3/2}$. Keywords:Blaschke products, Hardy spaces, Bergman spaces Categories:30D50, 30D55, 32A36 |
3. CMB 2005 (vol 48 pp. 409)
The Existence of Universal Inner Functions on the Unit Ball of $\mathbb{C}^n$ It is shown that there exists an inner function
$I$ defined on the unit ball ${\bf B}^n$ of ${\mathbb C}^n$
such that each function holomorphic on ${\bf B}^n$ and
bounded by $1$ can be approximated by
``non-Euclidean translates" of $I$.
Keywords:universal inner functions Categories:32A35, 30D50, 47B38 |
4. CMB 2004 (vol 47 pp. 17)
Universal Singular Inner Functions We show that there exists a singular inner function $S$ which is
universal for noneuclidean translates; that is one for which the set
$\{S(\frac{z+z_n}{1+\bar z_nz}):n\in\mathbb{N}\}$ is locally uniformly dense
in the set of all zero-free holomorphic functions in $\mathbb{D}$ bounded by
one.
Category:30D50 |