On decompositions of trigonometric polynomials

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1 Scopus citations


Let Rt[θ] be the ring generated over R by cosθ and sinθ, and Rt(θ) be its quotient field. In this paper we study the ways in which an element p of Rt[θ] can be decomposed into a composition of functions of the form p = R ◦ q, where R ∈ R(x) and q ∈ Rt(θ). In particular, we describe all possible solutions of the functional equation R1 ◦ q1 = R2 ◦ q2, where R1,R2 ∈ R[x] and q1, q2 ∈ Rt[θ].

Original languageEnglish
Pages (from-to)337-353
Number of pages17
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - 1 Mar 2017

ASJC Scopus subject areas

  • General Mathematics


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