On the uniqueness of periodic decomposition

• Autorzy: Viktor Harangi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 39A70: Difference operators
• 39B22: Equations for real functions
• 26A99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 211
• Numer: 3
• Strony: 225-244

Daty

wydano

2011

Twórcy

autor

Viktor Harangi

• Department of Analysis, Eötvös Loránd University, Pázmány Péter sétány 1/c, H-1117 Budapest, Hungary

Identyfikatory

DOI

10.4064/fm211-3-2