Fourier dimension of random images
(2016) In Arkiv för Matematik 54(2). p.455-471- Abstract
Given a compact set of real numbers, a random Cm + α-diffeomorphism is constructed such that the image of any measure concentrated on the set and satisfying a certain condition involving a real number s, almost surely has Fourier dimension greater than or equal to s/ (m+ α). This is used to show that every Borel subset of the real numbers of Hausdorff dimension s is Cm + α-equivalent to a set of Fourier dimension greater than or equal to s/ (m+ α). In particular every Borel set is diffeomorphic to a Salem set, and the Fourier dimension is not invariant under Cm-diffeomorphisms for any m.
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https://lup.lub.lu.se/record/08c91cf1-fc98-460c-a304-893c220edf5a
- author
- Ekström, Fredrik LU
- organization
- publishing date
- 2016-10-01
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Arkiv för Matematik
- volume
- 54
- issue
- 2
- pages
- 17 pages
- publisher
- Springer
- external identifiers
-
- scopus:84979587640
- wos:000384531500011
- ISSN
- 0004-2080
- DOI
- 10.1007/s11512-016-0237-3
- language
- English
- LU publication?
- yes
- id
- 08c91cf1-fc98-460c-a304-893c220edf5a
- date added to LUP
- 2016-10-17 07:37:56
- date last changed
- 2025-03-23 23:44:04
@article{08c91cf1-fc98-460c-a304-893c220edf5a,
abstract = {{<p>Given a compact set of real numbers, a random C<sup>m</sup> <sup>+</sup> <sup>α</sup>-diffeomorphism is constructed such that the image of any measure concentrated on the set and satisfying a certain condition involving a real number s, almost surely has Fourier dimension greater than or equal to s/ (m+ α). This is used to show that every Borel subset of the real numbers of Hausdorff dimension s is C<sup>m</sup> <sup>+</sup> <sup>α</sup>-equivalent to a set of Fourier dimension greater than or equal to s/ (m+ α). In particular every Borel set is diffeomorphic to a Salem set, and the Fourier dimension is not invariant under C<sup>m</sup>-diffeomorphisms for any m.</p>}},
author = {{Ekström, Fredrik}},
issn = {{0004-2080}},
language = {{eng}},
month = {{10}},
number = {{2}},
pages = {{455--471}},
publisher = {{Springer}},
series = {{Arkiv för Matematik}},
title = {{Fourier dimension of random images}},
url = {{http://dx.doi.org/10.1007/s11512-016-0237-3}},
doi = {{10.1007/s11512-016-0237-3}},
volume = {{54}},
year = {{2016}},
}