Fourier dimension of random images

Summary, in English

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.

• Författare: Fredrik Ekström
• Avdelning/ar: Matematik LTH
• Publiceringsår: 2016-10-01
• Språk: Engelska
• Sidor: 455-471
• Publikation/Tidskrift/Serie: Arkiv för Matematik
• Volym: 54
• Issue: 2
• Länkar: http://dx.doi.org/10.1007/s11512-016-0237-3
• Dokumenttyp: Artikel i tidskrift
• Förlag: Springer
• Ämne: Mathematics
• Status: Published
• ISBN/ISSN/Övrigt: ISSN: 0004-2080