{"paper":{"title":"On measures which generate the scalar product in a space of rational functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.CV","authors_text":"Victor Katsnelson","submitted_at":"2016-02-07T14:49:57Z","abstract_excerpt":"Let $z_1,z_2,\\,\\ldots\\,,z_n$ be pairwise different points of the unit disc and $\\mathscr{L}(z_1,z_2,\\,\\ldots\\,z_n)$ be the linear space generated by the rational fractions $\\frac{1}{t-z_1} , \\frac{1}{t-z_2} , \\cdots\\ , \\frac{1}{t-z_n}\\cdot$ Every non-negative measure $\\sigma$ on the unit circle $\\mathbb{T}$ generates the scalar product \\[\\langle\\,f\\,,\\,g\\,\\rangle_{\\!_{L^2_\\sigma}} =\\int\\limits_{\\mathbb{T}}f(t)\\,\\bar{g(t)}\\,\\sigma(dt), \\quad \\forall\\,f,g\\,\\in\\,L^2_\\sigma.\\] The measures $\\sigma$ are described which satisfy the condition \\[\\langle\\,f\\,,\\,g\\,\\rangle_{\\!_{L^2_\\sigma}}= \\langle\\,f\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02745","kind":"arxiv","version":2},"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"}