{"paper":{"title":"On the integral functional equations: On the integral d'Alembert's and Wilson's functional equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Bouikhalene Belaid, Elqorachi Elhoucien","submitted_at":"2016-02-22T11:16:44Z","abstract_excerpt":"Let $G$ be a locally compact group, and let $K$ be a compact subgroup of $G$. Let $\\mu : G\\longrightarrow\\mathbb{C}\\backslash\\{0\\}$ be a character of $G$. In this paper, we deal with the integral equations $$W_{\\mu}(K):\\; \\;\\int_{K}f(xkyk^{-1})dk+\\mu(y)\\int_{K}f(xky^{-1}k^{-1})dk=2f(x)g(y),$$ and $$D_{\\mu}(K):\\; \\;\\int_{K}f(xkyk^{-1})dk+\\mu(y)\\int_{K}f(xky^{-1}k^{-1})dk=2f(x)f(y)$$ for all $x, y\\in G$ where $f, g: G\\longrightarrow \\mathbb{C}$, to be determined, are complex continuous functions on $G$.\n  When $K\\subset Z(G)$, the center of $G$, $D_{\\mu}(K)$ reduces to the new version of d'Almbe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02064","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"}