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arXiv · 1211.4803

On Fourier analytic properties of graphs

Jonathan M. Fraser·Tuomas Orponen·Tuomas Sahlsten
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Abstract

We study the Fourier dimensions of graphs of real-valued functions defined on the unit interval [0,1]. Our results imply that the graph of the fractional Brownian motion is almost surely not a Salem set, answering in part a question of Kahane from 1993, and that the graph of a Baire typical function in C[0,1] has Fourier dimension zero.

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Jonathan M. Fraser, Tuomas Orponen, Tuomas Sahlsten. 2013-01-20. On Fourier analytic properties of graphs. https://arxiv.org/abs/1211.4803

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