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Fourier asymptotics of statistically self-similar measures (1999)

Bluhm, Christian

Springer

The journal of Fourier analysis and applications 5 (1999), S. 355-362

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ISSN: 1531-5851

Keywords: 28A80 ; 42B10 ; 60G57 ; random self-similar measures ; Fourier dimension ; Salem sets

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01259376

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