{"paper":{"title":"Approximation numbers of composition operators on the Dirichlet space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Li (LML), Herv\\'e Queff\\'elec (LPP), Luis Rodriguez-Piazza, Pascal Lef\\`evre (LML)","submitted_at":"2012-12-18T14:44:27Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4366","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}