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Approximation numbers of composition operators on the Dirichlet space

Pascal Lefèvre Laboratoire de Mathématiques de Lens EA 2462, Fédération CNRS Nord-Pas-de-Calais FR 2956 Faculté des Sciences Jean Perrin, Université Lille-Nord-de-France UArtois Daniel Li Laboratoire de Mathématiques de Lens EA 2462, Fédération CNRS Nord-Pas-de-Calais FR 2956 Faculté des Sciences Jean Perrin, Université Lille-Nord-de-France UArtois Hervé Queffélec Laboratoire Paul Painlevé U.M.R. CNRS 8524, Université Lille-Nord-de-France USTL Luis Rodríguez-Piazza Facultad de Matemáticas, Departamento de Análisis Matemático & IMUS, Universidad de Sevilla

Functional Analysis mathscidoc: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.
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@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.
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