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.
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Communicated by Robert S. Strichartz
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Bluhm, C. Fourier asymptotics of statistically self-similar measures. The Journal of Fourier Analysis and Applications 5, 355–362 (1999). https://doi.org/10.1007/BF01259376
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DOI: https://doi.org/10.1007/BF01259376