Abstract
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.
Funding Statement
Partially supported by the Spanish research project MTM 2012-30748.
Citation
Pascal Lefèvre. Daniel Li. Hervé Queffélec. Luis Rodríguez-Piazza. "Approximation numbers of composition operators on the Dirichlet space." Ark. Mat. 53 (1) 155 - 175, April 2015. https://doi.org/10.1007/s11512-013-0194-z
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