Abstract
Let Sp ⊂ R+ be a discrete countable set, let {αλ}λ∈Sp be a sequence in l1(Sp) and f(x) ≔ ∑λ∈Spαλsin(λx). f is an almost periodic odd function with {λ: ±λ ∈ Sp} as spectrum. We give some conditions about the set S so that \(\int _1^{+\infty}\ f(x){\rm sin}(Rx){dx\over x}\rightarrow 0\) whenever R → +∞, R ∈ S.
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