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Approximation numbers of composition operators on the Dirichlet space


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Opened Access Approximation numbers of composition operators on the Dirichlet space

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Author: Lefèvre, Pascal
Li, Daniel
Queffélec, Hervé
Rodríguez Piazza, Luis
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2015-04
Published in: Arkiv för Matematik, 53 (1), 155-175.
Document type: Article
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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DOI: 10.1007/s11512-013-0194-z

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