Journal of Fourier Analysis and Applications

, Volume 5, Issue 4, pp 355–362

Fourier asymptotics of statistically self-similar measures

  • Christian Bluhm

DOI: 10.1007/BF01259376

Cite this article as:
Bluhm, C. The Journal of Fourier Analysis and Applications (1999) 5: 355. doi:10.1007/BF01259376


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 

Copyright information

© Birkhäuser Boston 1999

Authors and Affiliations

  • Christian Bluhm
    • 1
  1. 1.Mathematics DepartmentUniversity of GreifswaldGreifswaldGermany

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