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arXiv · 1812.08747

Fourier series in BMO with number theoretical implications

Fernando Chamizo·Antonio Córdoba·Adrián Ubis
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Abstract

We introduce an elementary argument to bound the $\textrm{BMO}$ seminorm of Fourier series with gaps giving in particular a sufficient condition for them to be in this space. Using finer techniques we carry out a detailed study of the series $\sum n^{-1}e^{2\pi i n^2 x}$ providing some insight into how much this $\text{BMO}$ Fourier series differs from defining an $L^\infty$ function.

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Fernando Chamizo, Antonio Córdoba, Adrián Ubis. 2018-12-20. Fourier series in BMO with number theoretical implications. https://arxiv.org/abs/1812.08747

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