Fourier dimension of random images

作者：Ekstrom Fredrik^*

来源：Arkiv for Matematik, 2016, 54(2): 455-471.

DOI：10.1007/s11512-016-0237-3

Given a compact set of real numbers, a random -diffeomorphism is constructed such that the image of any measure concentrated on the set and satisfying a certain condition involving a real number , almost surely has Fourier dimension greater than or equal to . This is used to show that every Borel subset of the real numbers of Hausdorff dimension is -equivalent to a set of Fourier dimension greater than or equal to . In particular every Borel set is diffeomorphic to a Salem set, and the Fourier dimension is not invariant under -diffeomorphisms for any .

• 出版日期2016-10