# On decompositions of trigonometric polynomials

Authors
Type
Preprint
Publication Date
Jul 22, 2013
Submission Date
Jul 22, 2013
Identifiers
arXiv ID: 1307.5594
Source
arXiv
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## Abstract

Let R_t[\theta] be the ring generated over R by cos\theta and sin\theta, and R_t(\theta) be its quotient field. In this paper we study the ways in which an element p of R_t[\theta] can be decomposed into a composition of functions of the form p=R(q), where R\in R(x) and q\in 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 R[x] and q_1,q_2\in R_t[\theta].

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