Zhiqiang Wang

activity

20192026

most citedSpectrality of random convolutions generated by finitely many Hadamard triples

16 citations · 31 across the 12 of their papers we have counts for

collaborators

13 papers

math.DS2026

Asymptotic separation of periodic orbits and fractal dimension

Derong Kong, Zhiqiang Wang, Daohua Yu

For a totally bounded metric dynamical system $(X, d, T)$ we introduce a new critical value $s (X, d, T)$ which quantifies the asymptotic separation of periodic orbits. Mo…

math.NT2025

Rational points in Cantor sets in the complex plane

Wenxia Li, Zhiqiang Wang, Jiuzhou Zhao

Let $K$ be an imaginary quadratic field and let $O_{K}$ be the ring of algebraic integers of $K$ . For $α \in O_{K}$ with $∣ α ∣ > 1$ , define \[ \mathcal{D}_α= \bigcup_…

math.CA2025

On the Eigen-Falconer theorem in $R^{d}$

Wenxia Li, Zhiqiang Wang, Jiayi Xu

In this paper, we study the analogous Erdős similarity conjecture in higher dimensions and generalize the Eigen-Falconer theorem. We show that if $A=\{\boldsymbol{x}_n\}_{n=1}^\inf…

math.CA2023

Fractal Sumset Properties

Derong Kong, Zhiqiang Wang

In this paper we introduce two notions of fractal sumset properties. A compact set $K \subset R^{d}$ is said to have the Hausdorff sumset property (HSP) if for any $\ell\in\ma…

math.DS2023

On the union of homogeneous symmetric Cantor set with its translations

Derong Kong, Wenxia Li, Zhiqiang Wang +2

Fix a positive integer $N$ and a real number $0 < β < 1/ (N + 1)$ . Let $Γ$ be the homogeneous symmetric Cantor set generated by the IFS $$ \Big\{ ϕ_i(x)=βx + i \frac{1-β}{N}: i=0,1,\cdo…

math.CA2022★ 3 cited

The Spectrality of Infinite Convolutions in $R^{d}$

Wenxia Li, Zhiqiang Wang

In this paper, we study the spectrality of infinite convolutions in $R^{d}$ , where the spectrality means the corresponding square integrable function space admits a family o…

math.CA2022★ 4 cited

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…

math.CA2022

Weak Convergence and Spectrality of Infinite Convolutions

Wenxia Li, Jun Jie Miao, Zhiqiang Wang

Let ${A_{k}}_{k = 1}^{\infty}$ be a sequence of finite subsets of $R^{d}$ satisfying that $# A_{k} \geq 2$ for all integers $k \geq 1$ . In this paper, we first give a sufficient a…

math.NT2022★ 4 cited

Rational Points in Translations of The Cantor Set

Kan Jiang, Derong Kong, Wenxia Li +1

Given two coprime integers $p \geq 2$ and $q \geq 3$ , let $D_{p} \subset [0, 1)$ consist of all rational numbers which have a finite $p$ -ary expansion, and let $$ K(q, \mathcal{A})=\bigg\{…

math.CA2022★ 16 cited

Spectrality of random convolutions generated by finitely many Hadamard triples

Wenxia Li, Jun Jie Miao, Zhiqiang Wang

Let ${(N_{j}, B_{j}, L_{j}) : 1 \leq j \leq m}$ be finitely many Hadamard triples in $R$ . Given a sequence of positive integers ${n_{k}}_{k = 1}^{\infty}$ and $ω=(ω_k)_{k=1}^\infty \…

math.DS2021

On a class of self-similar sets which contain finitely many common points

Kan Jiang, Derong Kong, Wenxia Li +1

For $λ \in (0, 1/2]$ let $K_{λ} \subset R$ be a self-similar set generated by the iterated function system ${λ x, λ x + 1 - λ}$ . Given $x \in (0, 1/2)$ , let $Λ (x)$ be the set of $λ\in(0…

math.DS2020★ 3 cited

On the sum of squares of middle-third Cantor set

Zhiqiang Wang, Kan Jiang, Wenxia Li +1

Let $C$ be the middle-third Cantor set. In this paper, we show that for every $x \in [0, 4]$ , there exist $x_{1}, x_{2}, x_{3}, x_{4} \in C$ such that $x = x_{1}^{2} + x_{2}^{2} + x_{3}^{2} + x_{4}^{2},$ which a…

math.NT2019★ 1 cited

Univoque bases of real numbers: local dimension, Devil's staircase and isolated points

Derong Kong, Wenxia Li, Fan Lv +2

Given a positive integer $M$ and a real number $x > 0$ , let $U (x)$ be the set of all bases $q \in (1, M + 1]$ for which there exists a unique sequence $(d_{i}) = d_{1} d_{2} \dots$ with…

Asymptotic separation of periodic orbits and fractal dimension

Rational points in Cantor sets in the complex plane

On the Eigen-Falconer theorem in Rd

Fractal Sumset Properties

On the union of homogeneous symmetric Cantor set with its translations

The Spectrality of Infinite Convolutions in Rd

Spectrality of Infinite Convolutions and Random Convolutions

Weak Convergence and Spectrality of Infinite Convolutions

Rational Points in Translations of The Cantor Set

Spectrality of random convolutions generated by finitely many Hadamard triples

On a class of self-similar sets which contain finitely many common points

On the sum of squares of middle-third Cantor set

Univoque bases of real numbers: local dimension, Devil's staircase and isolated points

On the Eigen-Falconer theorem in $R^{d}$

The Spectrality of Infinite Convolutions in $R^{d}$