{"paper":{"title":"Integral Van Vleck's and Kannappan's functional equations on semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Elqorachi Elhoucien","submitted_at":"2016-05-12T16:43:22Z","abstract_excerpt":"In this paper we study the solutions of the integral Van Vleck's functional equation for the sine $$\\int_{S}f(x\\tau(y)t)d\\mu(t)-\\int_{S}f(xyt)d\\mu(t) =2f(x)f(y),\\; x,y\\in S$$ and the integral Kannappan's functional equation $$\\int_{S}f(xyt)d\\mu(t)+\\int_{S}f(x\\tau(y)t)d\\mu(t) =2f(x)f(y),\\; x,y\\in S,$$ where $S$ is a semigroup, $\\tau$ is an involution of $S$ and $\\mu$ is a measure that is linear combinations of point measures $(\\delta_{z_{i}})_{i\\in I}$, such that for all $i\\in I$, $z_{i}$ is contained in the center of $S$. \\\\ We express the solutions of the first equation by means of multiplica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05248","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"}