# MathSciDoc: An Archive for Mathematician ∫

#### Functional Analysismathscidoc:1701.12014

Arkiv for Matematik, 49, (1), 1-16, 2009.3
It is shown that for any\$t\$, 0<\$t\$<∞, there is a Jordan arc Γ with endpoints 0 and 1 such that \$\Gamma\setminus\{1\}\subseteq\mathbb{D}:=\{z:|z|<1\}\$ and with the property that the analytic polynomials are dense in the Bergman space \$\mathbb{A}^{t}(\mathbb{D}\setminus\Gamma)\$ . It is also shown that one can go further in the Hardy space setting and find such a Γ that is in fact the graph of a continuous real-valued function on [0,1], where the polynomials are dense in \$H^{t}(\mathbb{D}\setminus\Gamma)\$ ; improving upon a result in an earlier paper.
```@inproceedings{john2009density,
title={Density of the polynomials in Hardy and Bergman spaces of slit domains},
author={John R. Akeroyd},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203628865667990},
booktitle={Arkiv for Matematik},
volume={49},
number={1},
pages={1-16},
year={2009},
}
```
John R. Akeroyd. Density of the polynomials in Hardy and Bergman spaces of slit domains. 2009. Vol. 49. In Arkiv for Matematik. pp.1-16. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203628865667990.