{"paper":{"title":"A Hankel matrix acting on spaces of analytic functions","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":"2017-06-12T13:18:42Z","abstract_excerpt":"If $\\mu $ is a positive Borel measure on the interval $[0, 1)$ we let $\\mathcal H_\\mu $ be the Hankel matrix $\\mathcal H_\\mu =(\\mu _{n, k})_{n,k\\ge 0}$ 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 $. This is a natural generalization of the classical Hilbert operator. In this pap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04079","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"}