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On the concept of inner function in Hardy and Bergman spaces in multiply connected domains
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 42019 (English)In: Analysis and Mathematical Physics, ISSN 1664-2368, E-ISSN 1664-235X, Vol. 9, no 2, p. 839-866Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2019. Vol. 9, no 2, p. 839-866
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Mathematics
Identifiers
URN: urn:nbn:se:su:diva-172050DOI: 10.1007/s13324-019-00319-5ISI: 000474521300011OAI: oai:DiVA.org:su-172050DiVA, id: diva2:1345070
Available from: 2019-08-22 Created: 2019-08-22 Last updated: 2019-08-22Bibliographically approved

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