Sums and products of periodic functions

Robert Deville

doi:10.2478/mjpaa-2023-0014

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Sums and products of periodic functions

Moroccan Journal of Pure and Applied Analysis

Volume 9 (2023): Issue 2 (May 2023)

By: Robert Deville

Open Access

|Jun 2023

Abstract

There exist two real valued periodic functions on the real line such that, for every x ∈ ℝ, f₁(x) + f₂(x) = x, but it is impossible to find two real valued periodic functions on the real line such that, for every x ∈ ℝ, f₁(x) + f₂(x) = x². 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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