Journal of Fourier Analysis and Applications

, Volume 5, Issue 4, pp 355–362

Fourier asymptotics of statistically self-similar measures

  • Christian Bluhm


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 


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Copyright information

© Birkhäuser Boston 1999

Authors and Affiliations

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

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