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

2010/07/18 by S. Favorov, Favorov, S., Leonid Golinskiĭ +1 · 1 citation
Mathematics · #30D50 #31A05 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1007.3020

openalex publication_date 2010/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 \citeFG. 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 \citeFG similar to the standard local Blaschke condition for analytic and bounded functions in the unit disk.

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• A Blaschke-type condition for analytic functions on finitely connected domains. Applications to complex perturbations of a finite-band selfadjoint operator

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