On the concept of inner function in Hardy and Bergman spaces in multiply connected domains

We discuss the notion of an inner function for spaces of analytic functions in multiply connected domains in C , giving a historical overview and comparing several possible definitions. We explore connections between inner functions, zero-divisors for Hardy spaces and Bergman spaces, and weighted re...

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Bibliographic Details
Published in:Analysis and mathematical physics 2019-06, Vol.9 (2), p.839-866
Main Authors: Bénéteau, Catherine, Fleeman, Matthew, Khavinson, Dmitry, Sola, Alan A.
Format: Article
Language:English
Subjects:
Analysis
Analytic functions
Domains
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Obstructions
Recording
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Summary:We discuss the notion of an inner function for spaces of analytic functions in multiply connected domains in C , giving a historical overview and comparing several possible definitions. We explore connections between inner functions, zero-divisors for Hardy spaces and Bergman spaces, and weighted reproducing kernels. After recording some obstructions and negative results, we suggest avenues for further research and point out several open problems.
ISSN:1664-2368
1664-235X
1664-235X
DOI:10.1007/s13324-019-00319-5