Fractal Dimensions and Divergence of Fourier Series

Abstract

We show that for any 1 ≤ s ≤ 2, there is a periodic continuous function f whose Fourier series is divergent at some point, and whose graph satisfies

$\text{dim}_{H}(\text{graph} \ f)=\text{dim}_{B}(\text{graph} \ f)=s.$

Keywords

Fractal dimensions / Fourier series / 28A80

References

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Peking University