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On Fourier analytic properties of graphs

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Author(s)

Jonathan M. Fraser, Tuomas Orponen, Tuomas Sahlsten

School/Research organisations

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 in C[0,1] has Fourier dimension 0.

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Original languageEnglish
Pages (from-to)2730-2745
Number of pages16
JournalInternational Mathematics Research Notices
Volume2014
Issue number10
Early online date8 Feb 2014
DOIs
Publication statusPublished - 2014

    Research areas

  • HAUSDORFF DIMENSION, FIELDS

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