On Fourier analytic properties of graphs

Jonathan M. Fraser; Tuomas Orponen; Tuomas Sahlsten

doi:10.1093/imrn/rnt015

On Fourier analytic properties of graphs

Jonathan M. Fraser, Tuomas Orponen^*, Tuomas Sahlsten

^*Corresponding author for this work

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	2730-2745
Number of pages	16
Journal	International Mathematics Research Notices
Volume	2014
Issue number	10
Early online date	8 Feb 2014
DOIs	https://doi.org/10.1093/imrn/rnt015
Publication status	Published - 2014

Keywords

HAUSDORFF DIMENSION
FIELDS

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title = "On Fourier analytic properties of graphs",

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.",

keywords = "HAUSDORFF DIMENSION, FIELDS",

author = "Fraser, \{Jonathan M.\} and Tuomas Orponen and Tuomas Sahlsten",

note = "This work is financially supported in part by an EPSRC doctoral training grant EP/P505097/1 ",

year = "2014",

doi = "10.1093/imrn/rnt015",

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AU - Fraser, Jonathan M.

AU - Orponen, Tuomas

AU - Sahlsten, Tuomas

N1 - This work is financially supported in part by an EPSRC doctoral training grant EP/P505097/1

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - HAUSDORFF DIMENSION

KW - FIELDS

UR - https://www.scopus.com/pages/publications/84900793753

U2 - 10.1093/imrn/rnt015

DO - 10.1093/imrn/rnt015

M3 - Article

SN - 1073-7928

VL - 2014

SP - 2730

EP - 2745

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 10

ER -

On Fourier analytic properties of graphs

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Keywords

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