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- W2963571788 abstract "Kaufman and Tsujii proved that the Fourier transform of self-similar measures has a power decay outside of a sparse set of frequencies. We present a version of this result for homogeneous self-similar measures, with quantitative estimates, and derive several applications: (1) non-linear smooth images of homogeneous self-similar measures have a power Fourier decay, (2) convolving with a homogeneous self-similar measure increases correlation dimension by a quantitative amount, (3) the dimension and Frostman exponent of (biased) Bernoulli convolutions tend to 1 as the contraction ratio tends to 1, at an explicit quantitative rate. © 2018, Annales Academiae Scientiarum Fennicae Mathematica." @default.
- W2963571788 created "2019-07-30" @default.
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- W2963571788 date "2018-08-01" @default.
- W2963571788 modified "2023-10-16" @default.
- W2963571788 title "Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images" @default.
- W2963571788 doi "https://doi.org/10.5186/aasfm.2018.4350" @default.
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