Fourier dimension of random images
(2016) In Arkiv for Matematik 54(2). p.455471 Abstract
Given a compact set of real numbers, a random C^{m} ^{+} ^{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 C^{m} ^{+} ^{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 C^{m}diffeomorphisms for any m.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/08c91cf1fc98460ca304893c220edf5a
 author
 Ekström, Fredrik ^{LU}
 organization
 publishing date
 20161001
 type
 Contribution to journal
 publication status
 published
 subject
 in
 Arkiv for Matematik
 volume
 54
 issue
 2
 pages
 17 pages
 publisher
 Springer
 external identifiers

 Scopus:84979587640
 ISSN
 00042080
 DOI
 10.1007/s1151201602373
 language
 English
 LU publication?
 yes
 id
 08c91cf1fc98460ca304893c220edf5a
 date added to LUP
 20161017 07:37:56
 date last changed
 20161017 07:37:56
@misc{08c91cf1fc98460ca304893c220edf5a, 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 = {00042080}, language = {eng}, month = {10}, number = {2}, pages = {455471}, publisher = {ARRAY(0x81d7e88)}, series = {Arkiv for Matematik}, title = {Fourier dimension of random images}, url = {http://dx.doi.org/10.1007/s1151201602373}, volume = {54}, year = {2016}, }