On the uniqueness of periodic decomposition

Viktor Harangi

Viktor Harangi

Fundamenta Mathematicae, Tome 215 (2011), p. 225-244 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $a ₁, . . ., a_{k}$ be arbitrary nonzero real numbers. An $(a ₁, . . ., a_{k})$ -decomposition of a function f:ℝ → ℝ is a sum $f ₁ + \dots + f_{k} = f$ where $f_{i} : ℝ \to ℝ$ is an $a_{i}$ -periodic function. Such a decomposition is not unique because there are several solutions of the equation $h ₁ + \dots + h_{k} = 0$ with $h_{i} : ℝ \to ℝ a_{i}$ -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 $(a ₁, . . ., a_{k})$ -decomposition is essentially unique. We characterize those periods for which essential uniqueness holds.

Publié le : 2011-01-01

Zbl 1221.39031

EUDML-ID : urn:eudml:doc:282793

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     author = {Viktor Harangi},
     title = {On the uniqueness of periodic decomposition},
     journal = {Fundamenta Mathematicae},
     volume = {215},
     year = {2011},
     pages = {225-244},
     zbl = {1221.39031},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm211-3-2}
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Viktor Harangi. On the uniqueness of periodic decomposition. Fundamenta Mathematicae, Tome 215 (2011) pp. 225-244. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm211-3-2/