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arXiv · 2407.19424

A Wiener-type theorem for arcs in the unit cirle

Huichi Huang
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Abstract

We prove a Wiener-type theorem for arcs in the unit circle which concerns express the measure of an arc in the unit circle via the measure's Fourier coefficients. Then we use it to give the Fourier series of the Cantor and to compute the local dimension of a measure satisfying certain conditions of Fourier coefficients.

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Huichi Huang. 2024-07-28. A Wiener-type theorem for arcs in the unit cirle. https://arxiv.org/abs/2407.19424

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