{"paper":{"title":"Approximation numbers of composition operators on $H^p$ spaces of Dirichlet series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Fr\\'ed\\'eric Bayart, Herv\\'e Queff\\'elec, Kristian Seip","submitted_at":"2014-06-02T17:06:44Z","abstract_excerpt":"By a theorem of Bayart, $\\varphi$ generates a bounded composition operator on the Hardy space $\\Hp$of Dirichlet series ($1\\le p<\\infty$) only if $\\varphi(s)=c_0 s+\\psi(s)$, where $c_0$ is a nonnegative integer and $\\psi$ a Dirichlet series with the following mapping properties: $\\psi$ maps the right half-plane into the half-plane $\\Real s >1/2$ if $c_0=0$ and is either identically zero or maps the right half-plane into itself if $c_0$ is positive. It is shown that the $n$th approximation numbers of bounded composition operators on $\\Hp$ are bounded below by a constant times $r^n$ for some $0<r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0445","kind":"arxiv","version":3},"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"}