Jingcheng Liu

activity

20132026

most citedSpectral property of self-affine measures on

R^{n}

35 citations · 194 across the 35 of their papers we have counts for

collaborators

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8 papers · 1 filter

math.FA2026

Spectrality of product-form self-similar measures and tiles

Jing-Cheng Liu, Jia-Jie Wang, Jia Zheng

This paper studies the Fourier properties of self-similar measures and tiles generated by digit sets of product-form. Let $0 < ρ < 1$ be a real number and let $D$ be the direct sum of…

math.FA2025

A class of spectral measures with $m$ -alternate contraction ratios in $R$

Jing-cheng Liu, Jia-jie Wang

For a Borel probability measure $μ$ on $R^{n}$ , it is called a spectral measure if the Hilbert space $L^{2} (μ)$ admits an orthogonal basis of exponential functions. In thi…

math.FA2024

Spectrality of alternating-sign Moran measures

Jun Jason Luo, Lin Mao, Jing-Cheng Liu

For $m\geq 2$, let $D_m=\{0,1,\ldots,m-1\}$. For each $k\geq 1$, consider the family of contractions \[ Φ_k=\{ϕ_{k,d}:d\in D_{n_k}\}, \qquad ϕ_{k,d}(x)=(-1)^d b_k^{-1}(x+d),…

math.FA2024

Spectrality of a class of moran measures on $R^{2}$

Jing-Cheng Liu, Qiao-Qin Liu, Jun Jason Luo +1

We investigate spectral properties of planar Moran measures $μ_{{M_{n}}, {D_{n}}}$ generated by sequences of expanding matrices ${M_{n}} \subset G L (2, Z)$ and digit sets $\{D…

math.FA2022

Fourier bases of a class of planar self-affine measures

Ming-Liang Chen, Jing-Cheng Liu, Zhi-Yong Wang

Let $μ_{M, D}$ be the planar self-affine measure generated by an expansive integer matrix $M \in M_{2} (Z)$ and a non-collinear integer digit set $D=\left\{\begin{pmatrix} 0\\0…

math.FA2020★ 2 cited

The spectrality of self-affine measure under the similarity transformation of $G L_{n} (p)$

Jing-Cheng Liu, Zhi-Yong Wang

Let $μ_{M, D}$ be the self-affine measure generated by an expanding integer matrix $M \in M_{n} (Z)$ and a finite digit set $D \subset Z^{n}$ . It is well known that the tw…

math.FA2018★ 1 cited

The cardinality of orthogonal exponentials of planar self-affine measures with three-element digit sets

Ming-Liang Chen, Jing-Cheng Liu

In this paper, we consider the planar self-affine measures $μ_{M, D}$ generated by an expanding matrix $M \in M_{2} (Z)$ and an integer digit set $ D=\left\{ {\left( {\begin{ar…

math.FA2016

Non-spectral problem for the planar self-affine measures

Jing-cheng Liu, Xin-han Dong, Jian-lin Li

In this paper, we consider the non-spectral problem for the planar self-affine measures $μ_{M, D}$ generated by an expanding integer matrix $M \in M_{2} (Z)$ and a finite digit…