{"paper":{"title":"Additive solvability and linear independence of the solutions of a system of functional equations","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AC","authors_text":"Eszter Gselmann, Zsolt P\\'ales","submitted_at":"2014-03-14T10:47:39Z","abstract_excerpt":"The aim of this paper is twofold. On one hand, the additive solvability of the system of functional equations \\[d_{k}(xy)=\\sum_{i=0}^{k}\\Gamma(i,k-i) d_{i}(x)d_{k-i}(y) \\qquad (x,y\\in \\R,\\,k\\in\\{0,\\ldots,n\\}) \\] is studied, where $\\Delta_n:=\\big\\{(i,j)\\in\\Z\\times\\Z\\mid 0\\leq i,j\\mbox{and}i+j\\leq n\\big\\}$ and $\\Gamma\\colon\\Delta_n\\to\\R$ is a symmetric function such that $\\Gamma(i,j)=1$ whenever $i\\cdot j=0$. On the other hand, the linear dependence and independence of the additive solutions $d_{0},d_{1},\\dots,d_{n}\\colon \\R\\to\\R$ of the above system of equations is characterized. As a consequen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3525","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"}