Hausdorff and Fourier dimension
There is no constraint on the relation between the Fourier and Hausdorff dimension of a set beyond the condition that the Fourier dimension must not exceed the Hausdorff dimension.
On the theorem of Ivasev-Musatov. II
As in Part I [Annales de l’Inst. Fourier, 27-3 (1997), 97-113], our object is to construct a measure whose support has Lebesgue measure zero, but whose Fourier transform drops away extremely fast.
Some results on Kronecker, Dirichlet and Helson sets
We construct the following: a perfect non Dirichlet set every proper closed subset of which is Kronecker, A weak Kronecker set which is not an set; an independent countable Dirichlet set which is not Kronecker; a collection of -disjoint Kronecker sets whose union is independent but Helson ; A countable collection of disjoint Kronecker sets whose union is closed and independent but not Helson: a perfect independent Dirichlet set which is not Helson.
On the theorem of Ivasev-Musatov. I
We give a new version of Ivasev-Musatov’s construction of a measure whose support has Lebesgue measure zero but whose Fourier transform drops away extremely rapidly.
On the representation of functions by trigonometric series
Page 1