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Groups of unitary composition operators on Hardy-Smirnov spaces


Authors: Gajath Gunatillake, Mirjana Jovovic and Wayne Smith
Journal: Proc. Amer. Math. Soc. 143 (2015), 2439-2449
MSC (2010): Primary 47B33; Secondary 30H10
DOI: https://doi.org/10.1090/S0002-9939-2015-12436-7
Published electronically: January 9, 2015
MathSciNet review: 3326026
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Abstract: Let $ \Omega $ be an open simply connected proper subset of the complex plane. We identify, up to isomorphism, which groups are possible for the group of unitary composition operators of a Hardy-Smirnov space defined on $ \Omega $. We also study the relationship between the geometry of $ \Omega $ and the corresponding group.


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Additional Information

Gajath Gunatillake
Affiliation: Department of Mathematics and Statistics, American University of Sharjah, UAE
Email: gajathg@gmail.com, mgunatillake@aus.edu

Mirjana Jovovic
Affiliation: Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822
Email: jovovic@math.hawaii.edu

Wayne Smith
Affiliation: Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822
Email: wayne@math.hawaii.edu

DOI: https://doi.org/10.1090/S0002-9939-2015-12436-7
Keywords: Composition operator, unitary operator, Hardy-Smirnov space.
Received by editor(s): July 19, 2013
Received by editor(s) in revised form: December 16, 2013
Published electronically: January 9, 2015
Additional Notes: The first author would like to thank the University of Hawaii at Manoa for its generosity in hosting him during the collaboration.
Communicated by: Pamela B. Gorkin
Article copyright: © Copyright 2015 American Mathematical Society