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April 2015 Approximation numbers of composition operators on the Dirichlet space
Pascal Lefèvre, Daniel Li, Hervé Queffélec, Luis Rodríguez-Piazza
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Ark. Mat. 53(1): 155-175 (April 2015). DOI: 10.1007/s11512-013-0194-z

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

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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

Information

Received: 5 February 2013; Published: April 2015
First available in Project Euclid: 30 January 2017

zbMATH: 1309.47022
MathSciNet: MR3319618
Digital Object Identifier: 10.1007/s11512-013-0194-z

Rights: 2014 © Institut Mittag-Leffler

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Vol.53 • No. 1 • April 2015
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