Abstract
Abstract There exist two real valued periodic functions on the real line such that, for every x ∈ ℝ, f 1(x) + f 2(x) = x, but it is impossible to find two real valued periodic functions on the real line such that, for every x ∈ ℝ, f 1(x) + f 2(x) = x 2. The purpose of this note is to prove this result and also to study the possibility of decomposing more general polynomials into sum of periodic functions.
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