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arXiv · 2303.10919

The Littlewood problem and non-harmonic Fourier series

Philippe Jaming·Karim Kellay·Chadi Saba
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Abstract

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 settingof trigonometric polynomials with non-integer frequencies.The result is a quantitative extension of a result by Nazarov and also covers a resultby Hudson and Leckband when the length of the interval goes to infinity.

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Philippe Jaming, Karim Kellay, Chadi Saba. 2023-03-20. The Littlewood problem and non-harmonic Fourier series. https://doi.org/10.1007/s00208-023-02692-w

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