# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc:1701.333014

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$H$^{∞}($D$).
@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/20170108203608689457823},
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/20170108203608689457823.