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On Fourier analytic properties of graphs

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Author(s)

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 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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Details

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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  1. Intermediate dimensions

    Falconer, K. J., Fraser, J. & Kempton, T. M. W., 6 Nov 2019, (Accepted/In press) In : Mathematische Zeitschrift. 19 p.

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  2. On the Hausdorff dimension of microsets

    Fraser, J. M., Howroyd, D. C., Käenmäki, A. & Yu, H., Nov 2019, In : Proceedings of the American Mathematical Society. 147, 11, p. 4921-4936 16 p.

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ID: 135292780

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