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dc.contributor.authorFraser, Jonathan MacDonald
dc.contributor.authorSahlsten, Tuomas
dc.identifier.citationFraser , J M & Sahlsten , T 2018 , ' On the Fourier analytic structure of the Brownian graph ' , Analysis & PDE , vol. 11 , no. 1 , pp. 115-132 .
dc.identifier.otherPURE: 251061378
dc.identifier.otherPURE UUID: f0b1237c-92f9-4d59-9612-959183b1bd4a
dc.identifier.otherScopus: 85032263781
dc.identifier.otherORCID: /0000-0002-8066-9120/work/58285483
dc.identifier.otherWOS: 000429119200003
dc.description.abstractIn a previous article (Int. Math. Res. Not. 2014:10 (2014), 2730–2745) T. Orponen and the authors proved that the Fourier dimension of the graph of any real-valued function on R is bounded above by 1. This partially answered a question of Kahane (1993) by showing that the graph of the Wiener process Wt (Brownian motion) is almost surely not a Salem set. In this article we complement this result by showing that the Fourier dimension of the graph of Wt is almost surely 1. In the proof we introduce a method based on Itô calculus to estimate Fourier transforms by reformulating the question in the language of Itô drift-diffusion processes and combine it with the classical work of Kahane on Brownian images.
dc.relation.ispartofAnalysis & PDEen
dc.rights© 2018, Mathematical Sciences Publishers. This work has been made available online in accordance with the publisher’s policies. This is the final published version of the work, which was originally published at
dc.subjectBrownian motionen
dc.subjectWiener processen
dc.subjectItô calculusen
dc.subjectItô drift-diffusion processen
dc.subjectFourier transformen
dc.subjectFourier dimensionen
dc.subjectSalem seten
dc.subjectQA Mathematicsen
dc.titleOn the Fourier analytic structure of the Brownian graphen
dc.typeJournal articleen
dc.contributor.sponsorThe Leverhulme Trusten
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.description.statusPeer revieweden

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