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

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