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1. CMB 2011 (vol 54 pp. 338)
SzegÃ¶'s Theorem and Uniform Algebras We study SzegÃ¶'s theorem for a uniform algebra.
In particular, we do it for the disc algebra or the bidisc algebra.
Keywords:SzegÃ¶'s theorem, uniform algebras, disc algebra, weighted Bergman space Categories:32A35, 46J15, 60G25 |
2. CMB 2010 (vol 53 pp. 311)
Remark on Zero Sets of Holomorphic Functions in Convex Domains of Finite Type We prove that if the $(1,1)$-current of integration on an analytic subvariety $V\subset D$ satisfies the uniform Blaschke condition, then $V$ is the zero set of a holomorphic function $f$ such that $\log |f|$ is a function of bounded mean oscillation in $bD$. The domain $D$ is assumed to be smoothly bounded and of finite d'Angelo type. The proof amounts to non-isotropic estimates for a solution to the $\overline{\partial}$-equation for Carleson measures.
Categories:32A60, 32A35, 32F18 |
3. 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 |
4. 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 |