Bibliographic Details
| Title: |
Fourier dimension of random images |
| Authors: |
Ekström, Fredrik |
| Source: |
Arkiv f\"or Matematik, volume 54, issue 2, 2016, 455-471 |
| Publication Year: |
2015 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Classical Analysis and ODEs |
| More Details: |
Given a compact set of real numbers, a random $C^{m + \alpha}$-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 $s / (m + \alpha)$. This is used to show that every Borel subset of the real numbers of Hausdorff dimension $s$ is $C^{m + \alpha}$-equivalent to a set of Fourier dimension greater than or equal to $s / (m + \alpha)$. In particular every Borel set is diffeomorphic to a Salem set, and the Fourier dimension is not invariant under $C^m$-diffeomorphisms for any $m$.
Comment: Minor improvements of exposition |
| Document Type: |
Working Paper |
| DOI: |
10.1007/s11512-016-0237-3 |
| Access URL: |
http://arxiv.org/abs/1506.00961 |
| Accession Number: |
edsarx.1506.00961 |
| Database: |
arXiv |
