<abstract xmlns="http://www.w3.org/1999/xhtml">

There exist two real valued periodic functions on the real line such that, for every <italic>x</italic> ∈ ℝ, <italic>f</italic>1(<italic>x</italic>) + <italic>f</italic>2(<italic>x</italic>) = <italic>x</italic>, but it is impossible to find two real valued periodic functions on the real line such that, for every <italic>x</italic> ∈ ℝ, <italic>f</italic>1(<italic>x</italic>) + <italic>f</italic>2(<italic>x</italic>) = <italic>x</italic>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.
</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.

Sums and products of periodic functions

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Sums and products of periodic functions"}

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...

Sums and products of periodic functions

Published Online: Jun 07, 2023

Page range: 204 - 208

Received: Sep 07, 2022

Accepted: Dec 07, 2022

DOI: https://doi.org/10.2478/mjpaa-2023-0014

Keywords
Periodic functions, Homogeneous linear differential equation

© 2023 Robert Deville, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Sums and products of periodic functions

Published Online: Jun 07, 2023

Page range: 204 - 208

Received: Sep 07, 2022

Accepted: Dec 07, 2022

DOI: https://doi.org/10.2478/mjpaa-2023-0014

KeywordsPeriodic functions, Homogeneous linear differential equation

© 2023 Robert Deville, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Periodic functions, Homogeneous linear differential equation