On the uniqueness of periodic decomposition

Viktor Harangi. "On the uniqueness of periodic decomposition." Fundamenta Mathematicae 211.3 (2011): 225-244. <http://eudml.org/doc/282793>.

@article{ViktorHarangi2011,
abstract = {Let $a₁, ..., a_k$ be arbitrary nonzero real numbers. An $(a₁, ..., a_k)$-decomposition of a function f:ℝ → ℝ is a sum $f₁ + ⋯ + f_k = f$ where $f_i: ℝ → ℝ$ is an $a_i$-periodic function. Such a decomposition is not unique because there are several solutions of the equation $h₁ + ⋯ + h_k = 0$ with $h_i : ℝ → ℝ a_i$-periodic. We will give solutions of this equation with a certain simple structure (trivial solutions) and study whether there exist other solutions or not. If not, we say that the $(a₁, ..., a_k)$-decomposition is essentially unique. We characterize those periods for which essential uniqueness holds.},
author = {Viktor Harangi},
journal = {Fundamenta Mathematicae},
keywords = {periodic and almost periodic functions; functional equations; planar triple of reals; vector spaces over },
language = {eng},
number = {3},
pages = {225-244},
title = {On the uniqueness of periodic decomposition},
url = {http://eudml.org/doc/282793},
volume = {211},
year = {2011},
}

TY - JOUR
AU - Viktor Harangi
TI - On the uniqueness of periodic decomposition
JO - Fundamenta Mathematicae
PY - 2011
VL - 211
IS - 3
SP - 225
EP - 244
AB - Let $a₁, ..., a_k$ be arbitrary nonzero real numbers. An $(a₁, ..., a_k)$-decomposition of a function f:ℝ → ℝ is a sum $f₁ + ⋯ + f_k = f$ where $f_i: ℝ → ℝ$ is an $a_i$-periodic function. Such a decomposition is not unique because there are several solutions of the equation $h₁ + ⋯ + h_k = 0$ with $h_i : ℝ → ℝ a_i$-periodic. We will give solutions of this equation with a certain simple structure (trivial solutions) and study whether there exist other solutions or not. If not, we say that the $(a₁, ..., a_k)$-decomposition is essentially unique. We characterize those periods for which essential uniqueness holds.
LA - eng
KW - periodic and almost periodic functions; functional equations; planar triple of reals; vector spaces over
UR - http://eudml.org/doc/282793
ER -