{"paper":{"title":"A spectral radius type formula for approximation numbers of composition operators","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","submitted_at":"2014-07-08T16:57:01Z","abstract_excerpt":"For approximation numbers $a_n (C_\\phi)$ of composition operators $C_\\phi$ on weighted analytic Hilbert spaces, including the Hardy, Bergman and Dirichlet cases, with symbol $\\phi$ of uniform norm $< 1$, we prove that $\\lim_{n \\to \\infty} [a_n (C_\\phi)]^{1/n} = \\e^{- 1/ \\capa [\\phi (\\D)]}$, where $\\capa [\\phi (\\D)]$ is the Green capacity of $\\phi (\\D)$ in $\\D$. This formula holds also for $H^p$ with $1 \\leq p < \\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2171","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"}