{"paper":{"title":"On decompositions of trigonometric polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DS"],"primary_cat":"math.CA","authors_text":"F. Pakovich","submitted_at":"2013-07-22T05:48:43Z","abstract_excerpt":"Let $\\mathbb R_t[\\theta]$ be the ring generated over $\\mathbb R$ by $\\cos\\theta$ and $\\sin\\theta$, and $\\mathbb R_t(\\theta)$ be its quotient field. In this paper we study the ways in which an element p of $\\mathbb R_t[\\theta]$ can be decomposed into a composition of functions of the form $p=R(q),$ where $\\mathbb R\\in \\mathbb R(x)$ and $q\\in \\mathbb R_t(\\theta)$. In particular, we describe all possible solutions of the functional equation $R_1(q_1)=R_2(q_2)$, where $R_1, R_2 \\in \\mathbb R[x]$ and $q_1,q_2\\in \\mathbb R_t[\\theta].$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5594","kind":"arxiv","version":2},"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"}