Consider a1, . . . , an ∈ R arbitrary elements. We characterize those functions f : R → R that decompose into the sum of aj-periodic functions, i.e., f = f1+· · ·+fn with ∆aj f(x) := f(x+aj)−f(x) = 0. We show that f has such a decomposition if and only if for all partitions B1∪B2∪· · ·∪BN = {a1, . . . , an} with Bj consisting of commensurable elements with… (More)