On Fourier Analytic Properties of Graphs
/ Authors
/ 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 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 inC(0;1) has Fourier dimension zero.
Journal: International Mathematics Research Notices
DOI: 10.1093/IMRN/RNT015