{"paper":{"title":"A covariance equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"El Hassan Youssfi","submitted_at":"2018-10-23T09:48:02Z","abstract_excerpt":"Let $\\S$ be a commutative semigroup with identity $e$ and let $\\Gamma$ be a compact subset in the pointwise convergence topology of the space $\\S'$ of all non-zero multiplicative functions on $\\S.$ Given a continuous function $F: \\Gamma \\to \\mathbb C$ and a complex regular Borel measure $\\mu$ on $\\Gamma$ such that $\\mu(\\Gamma) \\not = 0.$ It is shown that $$ \\mu(\\Gamma) \\int_{\\Gamma} \\varrho(s) \\overline{\\varrho(t)} |F|^2(\\varrho) d\\mu(\\varrho) = \\int_{\\Gamma} \\varrho(s) F(\\varrho) d\\mu(\\varrho) \\int_{\\Gamma} \\overline{\\varrho(t) F(\\varrho)} d\\mu(\\varrho) $$ for all $(s, t) \\in \\S\\times \\S$ if "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09748","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"}