7 papers
Rational points in Cantor sets in the complex plane
Wenxia Li, Zhiqiang Wang, Jiuzhou Zhao
Let be an imaginary quadratic field and let be the ring of algebraic integers of . For with , define \[ \mathcal{D}_α= \bigc…
On the Eigen-Falconer theorem in
Wenxia Li, Zhiqiang Wang, Jiayi Xu
In this paper, we study the analogous ErdÅs similarity conjecture in higher dimensions and generalize the Eigen-Falconer theorem. We show that if $A=\{\boldsymbol{x}_n\}_{n=1}^\in…
The Spectrality of Infinite Convolutions in
Wenxia Li, Zhiqiang Wang
In this paper, we study the spectrality of infinite convolutions in , where the spectrality means the corresponding square integrable function space admits a family o…
Spectrality of Infinite Convolutions and Random Convolutions
Wenxia Li, Jun Jie Miao, Zhiqiang Wang
In this paper, we explore spectral measures whose square integrable spaces admit a family of exponential functions as an orthonormal basis.Our approach involves utilizing the integ…
Fractal Sumset Properties
Derong Kong, Zhiqiang Wang
In this paper we introduce two notions of fractal sumset properties. A compact set is said to have the Hausdorff sumset property (HSP) if for any $\ell\in\ma…
Rational Points in Translations of The Cantor Set
Kan Jiang, Derong Kong, Wenxia Li +1
Given two coprime integers and , let consist of all rational numbers which have a finite -ary expansion, and let $$ K(q, \mathcal{A})=\bigg\{…