{"paper":{"title":"Majoration of the dimension of the space of concatenated solutions of a specific pantograph equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jean-Fran\\c{c}ois Bertazzon","submitted_at":"2018-01-22T13:59:23Z","abstract_excerpt":"For each $\\lambda \\in \\mathbb N^*$, we consider the integral equation: \\[ \\int_{\\lambda y} ^{\\lambda x} f(t)\\, d t = f(x) - f(y) \\mbox{ for every $(x,y)\\in {\\mathbb R}_+^2$,} \\] where $f$ is the concatenation of two continuous functions $f_a,f_b:[0,\\lambda] \\rightarrow {\\mathbb R}$ along a word $u= u_0u_1\\cdots\\in\\{a,b\\}^{\\mathbb N}$ such that $u=\\sigma(u)$, where $\\sigma$ is a $\\lambda$-uniform substitution satisfying some combinatorial conditions.\n  There exists some non-trivial solutions. We show in this work that the dimension of the set of solutions is at most two."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07103","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"}