Approximation numbers of composition operators on the Dirichlet space
Functional Analysis
2012-12-19 v1
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.
Cite
@article{arxiv.1212.4366,
title = {Approximation numbers of composition operators on the Dirichlet space},
author = {Pascal Lefèvre and Daniel Li and Luis Rodriguez-Piazza and Hervé Queffélec},
journal= {arXiv preprint arXiv:1212.4366},
year = {2012}
}