{"paper":{"title":"Hankel matrices acting on the Hardy space $H^1$ and on Dirichlet spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Daniel Girela, Noel Merch\\'an","submitted_at":"2018-04-06T12:24:14Z","abstract_excerpt":"If $\\,\\mu \\,$ is a finite positive Borel measure on the interval $\\,[0,1)$, we let $\\,\\mathcal H_\\mu \\,$ be the Hankel matrix $\\,(\\mu _{n, k})_{n,k\\ge 0}\\,$ with entries $\\,\\mu _{n, k}=\\mu _{n+k}$, where, for $\\,n\\,=\\,0, 1, 2, \\dots $, $\\mu_n\\,$ denotes the moment of order $\\,n\\,$ of $\\,\\mu $. This matrix induces formally the operator $\\,\\mathcal{H}_\\mu (f)(z)= \\sum_{n=0}^{\\infty}\\left(\\sum_{k=0}^{\\infty} \\mu_{n,k}{a_k}\\right)z^n\\,$ on the space of all analytic functions $\\,f(z)=\\sum_{k=0}^\\infty a_kz^k\\,$, in the unit disc $\\,\\mathbb D $. When $\\,\\mu \\,$ is the Lebesgue measure on $\\,[0,1)\\,$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02227","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"}