On Fourier analytic properties of graphs
arXiv:1211.4803
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.
11 pages, 1 figure; references added and typos corrected in v2; to appear in Int. Math. Res. Not. IMRN