Abstract
Let Λ ⊂ ℝn be a uniformly discrete set and let CΛ be the vector space consisting of all mean periodic functions whose spectrum is simple and contained in Λ. If Λ is a gentle set then for every f ∈ CΛ we have f(x) = O(ωΛ(x)) as |x| → ∞ and ωΛ(x) can be estimated (Theorem 4.1). This line of research was proposed by Jean-Pierre Kahane in 1957.
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En hommage à mon ami Carlos Kenig
This work was supported by a grant from the Simons Foundation (Grant No. 601950 YM)
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Meyer, Y. Three Problems on Trigonometric Sums. Acta. Math. Sin.-English Ser. 35, 721–727 (2019). https://doi.org/10.1007/s10114-019-8416-3
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DOI: https://doi.org/10.1007/s10114-019-8416-3