Perfect fractal sets with zero Fourier dimension and arbitrarily long arithmetic progressions
Classical Analysis and ODEs
2017-07-21 v3
Abstract
By considering a Moran-type construction of fractals on , we show that for any , there exists some Moran fractal set, which is perfect, with Hausdorff dimension whose Fourier dimension is zero and it contains arbitrarily long arithmetic progressions.
Cite
@article{arxiv.1606.06684,
title = {Perfect fractal sets with zero Fourier dimension and arbitrarily long arithmetic progressions},
author = {Chun-Kit Lai},
journal= {arXiv preprint arXiv:1606.06684},
year = {2017}
}
Comments
Latest version and referee comments incorporated