{"paper":{"title":"Solutions and stability of a generalization of Wilson's equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bouikhalene Belaid, Elqorachi Elhoucien","submitted_at":"2015-05-14T10:20:31Z","abstract_excerpt":"In this paper we study the solutions and stability of the generalized Wilson's functional equation $\\int_{G}f(xty)d\\mu(t)+\\int_{G}f(xt\\sigma(y))d\\mu(t)=2f(x)g(y),\\; x,y\\in G$, where $G$ is a locally compact group, $\\sigma$ is a continuous involution of $G$ and $\\mu$ is an idempotent complex measure with compact support and which is $\\sigma$-invariant. We show that $\\int_{G}g(xty)d\\mu(t)+\\int_{G}g(xt\\sigma(y))d\\mu(t)=2g(x)g(y),\\; x,y\\in G$ if $f\\neq 0$ and $\\int_{G}f(t.)d\\mu(t)\\neq 0$. We also study some stability theorems of that equation and we establish the stability on noncommutaive groups "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06513","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"}