Limits of integrals involving almost periodic functions |
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Authors: | G. Molteni |
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Affiliation: | 1. Dipartimento di Matematica, Universitá di Milano, Via Saldini 50, 20133, Milano, Italy
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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 $int _1^{+infty} f(x){rm sin}(Rx){dxover x}rightarrow 0$ whenever R → +∞, R ∈ S. |
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