Article

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

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Abstract

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