Fourier series in BMO with number theoretical implications
Abstract
We introduce an elementary argument to bound the 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 Σ n-1e2π i n2 x providing some insight into how much this BMO Fourier series differs from defining an L∞ function.
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