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Projections in the space$H$^{∞}and the corona theorem for subdomains of coverings of finite bordered Riemann surfaces

Alexander Brudnyi Department of Mathematics and Statistics, University of Calgary

TBD mathscidoc:1701.333023

Arkiv for Matematik, 42, (1), 31-59, 2002.12
Let$M$be a non-compact connected Riemann surface of a finite type, and$R$⋐$M$be a relatively compact domain such that$H$_{1}($M$,$Z$)=$H$_{1}($R$,$Z$). Let $$\tilde R \to R$$ be a covering. We study the algebra$H$^{∞}($U$) of bounded holomorphic functions defined in certain subdomains $$U \subset \tilde R$$ . Our main result is a Forelli type theorem on projections in$H$^{∞}($D$).
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@inproceedings{alexander2002projections,
  title={Projections in the space$H$^{∞}and the corona theorem for subdomains of coverings of finite bordered Riemann surfaces},
  author={Alexander Brudnyi},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203609949260832},
  booktitle={Arkiv for Matematik},
  volume={42},
  number={1},
  pages={31-59},
  year={2002},
}
Alexander Brudnyi. Projections in the space$H$^{∞}and the corona theorem for subdomains of coverings of finite bordered Riemann surfaces. 2002. Vol. 42. In Arkiv for Matematik. pp.31-59. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203609949260832.
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