Zero sets of holomorphic functions in the bidisk

Zero sets of holomorphic functions in the bidisc

In this work we characterize the zero sets of holomorphic functions f in the bidisc such that log jf j Lp D p Moreover we give a su cient condition on a analytic variety to be de ned by a function in A D Introduction In this paper we study some geometrical conditions on analytic varieties in the bidisc D fz C jz j jz j g to be de ned by an holomorphic func tion with some restriction on its grow...

On the zero sets of bounded holomorphic functions in the bidisc

In this work we prove in a constructive way a theorem of Rudin which says that ifE is an analytic subset of the bidiscD with multiplicities which does not intersect a neighbourhood of the distinguished boundary then E is the zero set with multiplicities of a bounded holomorphic function This approach allows us to generalize this theorem and also some results obtained by P S Chee

Norm preserving extensions of holomorphic functions from subvarieties of the bidisk

Zero Sets for Spaces of Analytic Functions

We show that under mild conditions, a Gaussian analytic function F that a.s. does not belong to a given weighted Bergman space or Bargmann–Fock space has the property that a.s. no non-zero function in that space vanishes where F does. This establishes a conjecture of Shapiro (1979) on Bergman spaces and allows us to resolve a question of Zhu (1993) on Bargmann–Fock spaces. We also give a simila...

Maximal cluster sets on spaces of holomorphic functions

In this paper, which has an expository nature, we consider the so called cluster sets, that is the set of accumulation points of the set of values taken by a (usually, holomorphic) function on prescribed subsets. We are specially interested in the action of holomorphic operators in order to obtain maximal cluster sets, see below for details. Extensions of classical cluster sets, where they are ...