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Pré-Publication, Document De Travail Année : 2023

The Littlewood problem and non-harmonic Fourier series

Karim Kellay
Chadi Saba

Résumé

In this paper, we give a direct quantitative estimate of $L^1$ norms of non-harmonic trigonometric polynomials over large enough intervals. This extends the result by Konyagin and Mc Gehee, Pigno, Smith to the setting of trigonometric polynomials with non-integer frequencies. The result is a quantitative extension of a result by Nazarov and also covers a result by Hudson and Leckband when the length of the interval goes to infinity.
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Dates et versions

hal-04033535 , version 1 (17-03-2023)
hal-04033535 , version 2 (18-07-2023)

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Philippe Jaming, Karim Kellay, Chadi Saba. The Littlewood problem and non-harmonic Fourier series. 2023. ⟨hal-04033535v2⟩

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