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arXiv · 1212.4366

Approximation numbers of composition operators on the Dirichlet space

Pascal Lefèvre·Daniel Li·Luis Rodriguez-Piazza·Hervé Queffélec
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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 O. El-Fallah, K. Kellay, M. Shabankhah and A. Youssfi, on the set of contact points with the unit circle of a compact symbolic composition operator acting on the Dirichlet space 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 sub-exponentially small.

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Pascal Lefèvre, Daniel Li, Luis Rodriguez-Piazza, Hervé Queffélec. 2012-12-18. Approximation numbers of composition operators on the Dirichlet space. https://arxiv.org/abs/1212.4366

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