Journal of Fourier Analysis and Applications

, Volume 5, Issue 4, pp 355-362

First online:

Fourier asymptotics of statistically self-similar measures

  • Christian BluhmAffiliated withMathematics Department, University of Greifswald

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


In this paper we investigate the pointwise Fourier decay of some selfsimilar random measures. As an application we construct statistically selfsimilar Salem sets. For example, our result shows that a “slight” random perturbation of the classical Cantor set becomes a “nice” set in the sense that its Fourier dimension equals its Hausdorff dimension.

Math Subject Classifications

28A80 42B10 60G57

Keywords and phrases

random self-similar measures Fourier dimension Salem sets