X. Dai

activity

20122026

most citedThe

ab c

-problem for Gabor systems

25 citations · 25 across the 7 of their papers we have counts for

collaborators

7 papers

math.NT2026

Metric results for dyadic approximation on the middle-third Cantor set

Xin-Rong Dai, Bing Li, Bo Wang +1

Let $C$ be the middle-third Cantor set and $μ$ be the Cantor-Lebesgue measure on $C$ . A conjecture of Velani states that $μ (W_{2} (τ)) = 0$ if $τ > 1$ and $μ (W_{2} (τ)) = 1$ if $0 < τ \leq 1$ , wh…

math.FA2022

Frame set for Gabor systems with Haar window

Xin-Rong Dai, Meng Zhu

We show the full structure of the frame set for the Gabor system $G (g; α, β) := {e^{- 2 π im β \cdot} g (\cdot - n α) : m, n \in Z}$ with the window being the Haar function $g=-χ_{[…

math.FA2014

Spectral measures with arbitrary Hausdorff dimensions

Xin-Rong Dai, Qiyu Sun

In this paper, we consider spectral properties of Riesz product measures supported on homogeneous Cantor sets and we show the existence of spectral measures with arbitrary Hausdorf…

math.FA2014

On Spectral N-Bernoulli Mmeasure

Xin-Rong Dai, Xing-Gang He, Ka-Sing Lau

For $0 < ρ < 1$ and $N > 1$ an integer, let $μ$ be the self-similar measure defined by $μ (\cdot) = \sum_{i = 0}^{N - 1} \frac{1}{N} μ (ρ^{- 1} (\cdot) - i)$ . We prove that $L^{2} (μ)$ has an exponential or…

math.FA2014

Spectra of Cantor measures

Xinrong Dai

Let $μ_{q, b}$ be the Cantor measure associated with the iterated function system $f_{i} (x) = x / b + i / q, 0 \leq i \leq q - 1$ , where $2 \leq q, b / q \in Z$ . In this paper, we consider spectra and…

cs.IT2013★ 25 cited

The $ab c$ -problem for Gabor systems

Xin-Rong Dai, Qiyu Sun

A Gabor system generated by a window function $ϕ$ and a rectangular lattice $a Z \times Z / b$ is given by $${\mathcal G}(ϕ, a \Z\times \Z/b):=\{e^{-2πi n t/b} ϕ(t- m a):\ (m, n)\in…

math.FA2012

Spectral property of Cantor measures with consecutive digits

Xin-Rong Dai, Xing-Gang He, Chun-Kit Lai

We consider equally-weighted Cantor measures $μ_{q, b}$ arising from iterated function systems of the form $b^{- 1} (x + i)$ , $i = 0, 1, ..., q - 1$ , where $q < b$ . We classify the $(q, b)$ so…

Metric results for dyadic approximation on the middle-third Cantor set

Frame set for Gabor systems with Haar window

Spectral measures with arbitrary Hausdorff dimensions

On Spectral N-Bernoulli Mmeasure

Spectra of Cantor measures

The abc-problem for Gabor systems

Spectral property of Cantor measures with consecutive digits

The $ab c$ -problem for Gabor systems