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arXiv · 1906.12164

Fourier decay for self-similar measures

Boris Solomyak
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Abstract

We prove that, after removing a zero Hausdorff dimension exceptional set of parameters, all self-similar measures on the line have a power decay of the Fourier transform at infinity. In the homogeneous case, when all contraction ratios are equal, this is essentially due to Erd\H{o}s and Kahane. In the non-homogeneous case the difficulty we have to overcome is the apparent lack of convolution structure.

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Boris Solomyak. 2019-06-28. Fourier decay for self-similar measures. https://arxiv.org/abs/1906.12164

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