The Fourier dimension of Brownian limsup fractals
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Authors
Potgieter, Paul
Issue Date
2013
Type
Article
Language
en
Keywords
Brownian motion, Rapid points, Hausdorff dimension, Fourier dimension, Salem set
Alternative Title
Abstract
Robert Kaufman’s proof that the set of rapid points of Brownian motion has a Fourier dimension equal to its Hausdorff dimension was first published in 1974. A study of the proof of the original paper revealed several gaps in the arguments and a slight inaccuracy in the main theorem. This paper presents a new version of the construction and incorporates some recent results in order to establish a corrected version of Kaufman’s theorem. The method of proof can then be extended to show that functionally determined rapid points of Brownian motion also form Salem sets for absolutely continuous functions of finite energy.
Description
Citation
Potgieter, P. (2013). The Fourier dimension of Brownian limsup fractals. arXiv preprint arXiv
Publisher
Springer
License
Journal
Volume
Issue
PubMed ID
DOI
ISSN
1303-0678