# MathSciDoc: An Archive for Mathematician ∫

#### Functional Analysismathscidoc:1701.12026

Arkiv for Matematik, 53, (1), 155-175, 2013.2
We study the decay of approximation numbers of compact composition operators on the Dirichlet space. We give upper and lower bounds for these numbers. In particular, we improve on a result of El-Fallah, Kellay, Shabankhah and Youssfi, on the set of contact points with the unit circle of a compact symbolic composition operator acting on the Dirichlet space $\mathcal{D}$ . We extend their results in two directions: first, the contact only takes place at the point 1. Moreover, the approximation numbers of the operator can be arbitrarily subexponentially small.
@inproceedings{pascal2013approximation,
title={Approximation numbers of composition operators on the Dirichlet space},
author={Pascal Lefèvre, Daniel Li, Hervé Queffélec, and Luis Rodríguez-Piazza},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203638907293070},
booktitle={Arkiv for Matematik},
volume={53},
number={1},
pages={155-175},
year={2013},
}

Pascal Lefèvre, Daniel Li, Hervé Queffélec, and Luis Rodríguez-Piazza. Approximation numbers of composition operators on the Dirichlet space. 2013. Vol. 53. In Arkiv for Matematik. pp.155-175. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203638907293070.