Fourier decay for self-similar measures
Dynamical Systems
2020-06-23 v2 Classical Analysis and ODEs
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.
Cite
@article{arxiv.1906.12164,
title = {Fourier decay for self-similar measures},
author = {Boris Solomyak},
journal= {arXiv preprint arXiv:1906.12164},
year = {2020}
}
Comments
minor corrections, references added, results unchanged