Blaschke-type conditions for analytic functions in the unit disk: inverse problems and local analogs

Details Blaschke-type conditions for analytic functions in the unit disk: inverse problems and local analogs Blaschke-type conditions for analytic functions in the unit disk: inverse problems and local analogs

2010-07-18

arxiv.org/abs/1007.3020v1

Mathematics

Complex Variables

14 pages in LaTeX

Scientific paper

We continue the study of analytic functions in the unit disk of finite order with arbitrary set of singular points on the unit circle, introduced in \cite{FG}. The main focus here is made upon the inverse problem: the existence of a function from this class with a given singular set and zero set subject to certain Blaschke-type condition. We also discuss the local analog of the main result from \cite{FG} similar to the standard local Blaschke condition for analytic and bounded functions in the unit disk.

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