Abstract
Let R t [θ] be the ring generated over R by cosθ and sinθ, and R t (θ) be its quotient field. In this paper we study the ways in which an element p of R t [θ] can be decomposed into a composition of functions of the form p = R ◦ q, where R ∈ R(x) and q ∈ R t (θ). In particular, we describe all possible solutions of the functional equation R 1 ◦ q 1 = R 2 ◦ q 2, where R 1,R 2 ∈ R[x] and q 1, q 2 ∈ R t [θ].
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Pakovich, F. On decompositions of trigonometric polynomials. Isr. J. Math. 217, 337–353 (2017). https://doi.org/10.1007/s11856-017-1449-3
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DOI: https://doi.org/10.1007/s11856-017-1449-3