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Algebra i Analiz, 2022, Volume 34, Issue 3, Pages 159–174 (Mi aa1813)  
Research Papers

On the maximal ideal spaces of $\mathbf{H^\infty}$ on coverings of bordered Riemann surfaces

A. Brudnyi

Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4
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Abstract: The paper describes the topological structure of the maximal ideal space of the algebra of bounded holomorphic functions on a covering of a bordered Riemann surface. Some applications of the obtained results to the theory of bounded operator-valued holomorphic functions on Riemann surfaces are presented.
Keywords: maximal ideal space, interpolating sequence, Blaschke product, Gleason part, analytic disk, covering dimension, cohomology, Freudenthal compactification.
Funding agency Grant number
Natural Sciences and Engineering Research Council of Canada (NSERC)
Research is supported in part by NSERC.
Received: 19.08.2021
English version:
St. Petersburg Mathematical Journal, 2023, Volume 34, Issue 3, Pages 427–438
DOI: https://doi.org/10.1090/spmj/1761
Bibliographic databases:
Document Type: Article
Language: English
Citation: A. Brudnyi, “On the maximal ideal spaces of $\mathbf{H^\infty}$ on coverings of bordered Riemann surfaces”, Algebra i Analiz, 34:3 (2022), 159–174; St. Petersburg Math. J., 34:3 (2023), 427–438
Citation in format AMSBIB
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\by A.~Brudnyi
\paper On the maximal ideal spaces of $\mathbf{H^\infty}$ on coverings of bordered Riemann surfaces
\jour Algebra i Analiz
\yr 2022
\vol 34
\issue 3
\pages 159--174
\mathnet{http://mi.mathnet.ru/aa1813}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4022002}
\transl
\jour St. Petersburg Math. J.
\yr 2023
\vol 34
\issue 3
\pages 427--438
\crossref{https://doi.org/10.1090/spmj/1761}
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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