Perfect fractal sets with zero Fourier dimension and arbitrarily long arithmetic progressions
Perfect fractal sets with zero Fourier dimension and arbitrarily long arithmetic progressions
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DOI：
10.5186/aasfm.2017.4263
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发表时间：
2016-06
期刊：
影响因子：
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通讯作者：
Chun-Kit Lai
中科院分区：
文献类型：
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作者：
Chun-Kit Lai
通过研究$[0，1]$上Moran型分形的构造，证明了对于任意的$0\le s\le 1$，存在一个完备的Moran分形集，其Hausdorff维数s$的Fourier维数为零，且包含任意长的算术级数.
By considering a Moran-type construction of fractals on $[0,1]$, we show that for any $0\le s\le 1$, there exists some Moran fractal set, which is perfect, with Hausdorff dimension $s$ whose Fourier dimension is zero and it contains arbitrarily long arithmetic progressions.