Chun-Kit Lai

activity

20112026

most citedSome reductions of the spectral set conjecture to integers

34 citations · 105 across the 45 of their papers we have counts for

collaborators

49 papers

math.CA2026

The Kakeya problem for codimension-two planes in $R^{n}$

Chun-Kit Lai, Yixuan Pang, Rahul Sethi +1

We study the $(n - 2)$ -plane Kakeya problem in $R^{n}$ ( $n \geq 4$ ) subject to convex Wolff axioms. In other words, we study finite families of $δ$ -neighborhoods of $(n - 2)$ -plan…

math.CA2026

Weak Tiling by Unions of Non-overlapping Unit Cubes

Tianyu Chen, Shilei Fan, Mihail N. Kolountzakis +1

We study weak tiling by finite unions of pairwise non-overlapping unit cubes in $R^{d}$ that are not necessarily axis-parallel. We obtain a weak-tiling analogue of Keller's c…

math.CA2026

A new type of deterministic Salem sets and its spectrality

Chun-Kit Lai, Ruxi Shi, Yu-Hao Xie

For all $0 < s \leq 1$ , we provide a new deterministic construction of Cantor sets whose Fourier dimension and Hausdorff dimension are both equal to $s$ . The construction is based on…

math.CA2026

Spectrality of factors of product spectral measures

Mihail N. Kolountzakis, Chun-Kit Lai, Kailing Lai +1

We refine the method by Greenfeld and Lev for the product spectral set problem and generalize the theorem to a singular measure setting. Furthermore, we establish a new class of sp…

math.CA2026

On Constructions of full-dimensional absolutely normal sets of uniqueness

Chun-Kit Lai, Yu-Hao Xie

We construct a class of homogeneous Cantor-Moran measures with all contraction ratios being reciprocals of integers, and prove that they are pointwise absolutely normal. Our approa…

math.DS2025

Distinct dimensions for attractors of bi-Lipschitz iterated function systems

Simon Baker, Amlan Banaji, De-Jun Feng +2

In this paper, we construct an iterated function system on the line consisting of two bi-Lipschitz contractions whose attractor has distinct lower, Hausdorff, lower box, upper box,…

math.CA2025

Non-spectrality of some piecewise smooth curves and unions of line segments

Mihail N. Kolountzakis, Chun-Kit Lai

We develop a systematic study about the spectrality of measures supported on piecewise smooth curves by studying the support of the tempered distributions arising from the tiling e…

math.CA2025

A non-sticky Kakeya set of Lebesgue measure zero

Chun-Kit Lai, Adeline E. Wong

The Kakeya set conjecture in $R^{3}$ was recently resolved by Wang and Zahl. The distinction between sticky and non-sticky Kakeya sets plays an important role in their pro…

math.PR2025

Fourier dimension of the graph of fractional Brownian motion with $H \geq 1/2$

Chun-Kit Lai, Cheuk Yin Lee

We prove that the Fourier dimension of the graph of fractional Brownian motion with Hurst index greater than $1/2$ is almost surely 1. This extends the result of Fraser and Sahlste…

math.CA2025

When is the fractal uncertainty principle for discrete Cantor sets most uncertain?

Chun-Kit Lai, Ruxi Shi

We give a necessary and sufficient condition to achieve the most uncertain exponent in the fractal uncertainty principle of discrete Cantor sets. The condition will be described as…

math.CA2022★ 1 cited

Classification of spectral self-similar measures with four-digit elements

Li-Xiang An, Xinggang He, Chun-Kit Lai

Let $μ$ be a self-similar measure generated by iterated function system of four maps of equal contraction ratio $0 < ρ < 1$ . We study when $μ$ is a spectral measure which means that it…

math.CA2022

Product-form Hadamard triples and its spectral self-similar measures

Li-Xiang An, Chun-Kit Lai

In a previous work by Łaba and Wang, it was proved that whenever there is a Hadamard triple $(N, D, L)$ , then the associated one-dimensional self-similar measur…

math.CA2022

On a topological Erdős similarity problem

John Gallagher, Chun-Kit Lai, Eric Weber

A pattern is called universal in another collection of sets, when every set in the collection contains some linear and translated copy of the original pattern. Paul Erdős proposed…

math.CA2022★ 1 cited

Large sets avoiding affine copies of infinite sequences

Angel Cruz, Chun-Kit Lai, Malabika Pramanik

A conjecture of Erdős states that for any infinite set $A \subseteq R$ , there exists $E \subseteq R$ of positive Lebesgue measure that does not contain any nontrivi…

math.PR2021

Hausdorff and Fourier dimension of graph of continuous additive processes

Dexter Dysthe, Chun-Kit Lai

An additive process is a stochastic process with independent increments and that is continuous in probability. In this paper, we study the almost sure Hausdorff and Fourier dimensi…

math.FA2020

On exponential bases and frames with non-linear phase functions and some applications

Jean-Pierre Gabardo, Chun-Kit Lai, Vignon Oussa

In this paper, we study the spectrality and frame-spectrality of exponential systems of the type $E (Λ, φ) = {e^{2 π iλ \cdot φ (x)} : λ \in Λ}$ where the phase function $φ$ is a Borel me…

math.FA2020★ 1 cited

Arbitrarily sparse spectra for self-affine spectral measures

Li-Xiang An, Chun-Kit Lai

Given an expansive matrix $R \in M_{d} (Z)$ and a finite set of digit $B$ taken from $Z^{d} / R (Z^{d})$ . It was shown previously that if we can find an $L$ suc…

math.FA2020

Spectral properties of some unions of linear spaces

Chun-Kit Lai, Bochen Liu, Hal Prince

We consider \textit{additive spaces}, consisting of two intervals of unit length or two general probability measures on $R^{1}$ , positioned on the axes in $R^{2}$ ,…

math.CA2020

A proof of the Erdös similarity conjecture

Angel Cruz, Chun-Kit Lai, Malabika Pramanik

We show that for any infinite set $A$ in $R$ , there exists a compact set $E \subseteq R$ of positive Lebesgue measure that does not contain any non-trivial affin…

cs.IT2019

Conjugate Phase Retrieval in Paley-Wiener Space

Chun-Kit Lai, Friedrich Littmann, Eric Weber

We consider the problem of conjugate phase retrieval in Paley-Wiener space $P W_{π}$ . The goal of conjugate phase retrieval is to recover a signal $f$ from the magnitudes of linear me…

math.FA2019★ 1 cited

Spectrum is rational in dimension one

Chun-Kit Lai, Yang Wang

A bounded measurable set $Ω \subset R^{d}$ is called a spectral set if it admits some exponential orthonormal basis ${e^{2 π i ⟨ λ, x ⟩} : λ \in Λ}$ for $L^{2} (Ω)$ . In th…

math.CA2019

Fourier frames for surface-carried measures

Alex Iosevich, Chun-Kit Lai, Bochen Liu +1

In this paper we show that the surface measure on the boundary of a convex body of everywhere positive Gaussian curvature does not admit a Fourier frame. This answers a question pr…

math.CA2019★ 1 cited

On Spectral Cantor-Moran measures and a variant of Bourgain's sum of sine problem

Li-Xiang An, Xiaoye Fu, Chun-Kit Lai

In this paper, we show that if we have a sequence of Hadamard triples ${(N_{n}, B_{n}, L_{n})}$ with $B_{n} \subset {0, 1, .., N_{n} - 1}$ for $n = 1, 2, ...$ , except an extreme case, then the assoc…

math.FA2018★ 2 cited

Existence and exactness of exponential Riesz sequences and frames for fractal measures

Dorin Ervin Dutkay, Shahram Emami, Chun-Kit Lai

We study the construction of exponential frames and Riesz sequences for a class of fractal measures on $R^{d}$ generated by infinite convolution of discrete measures using…

The Kakeya problem for codimension-two planes in Rn

Weak Tiling by Unions of Non-overlapping Unit Cubes

A new type of deterministic Salem sets and its spectrality

Spectrality of factors of product spectral measures

On Constructions of full-dimensional absolutely normal sets of uniqueness

Distinct dimensions for attractors of bi-Lipschitz iterated function systems

Non-spectrality of some piecewise smooth curves and unions of line segments

A non-sticky Kakeya set of Lebesgue measure zero

Fourier dimension of the graph of fractional Brownian motion with H≥1/2

When is the fractal uncertainty principle for discrete Cantor sets most uncertain?

Classification of spectral self-similar measures with four-digit elements

Product-form Hadamard triples and its spectral self-similar measures

On a topological Erdős similarity problem

Large sets avoiding affine copies of infinite sequences

Hausdorff and Fourier dimension of graph of continuous additive processes

On exponential bases and frames with non-linear phase functions and some applications

Arbitrarily sparse spectra for self-affine spectral measures

Spectral properties of some unions of linear spaces

A proof of the Erdös similarity conjecture

Conjugate Phase Retrieval in Paley-Wiener Space

Spectrum is rational in dimension one

Fourier frames for surface-carried measures

On Spectral Cantor-Moran measures and a variant of Bourgain's sum of sine problem

Existence and exactness of exponential Riesz sequences and frames for fractal measures

The Kakeya problem for codimension-two planes in $R^{n}$

Fourier dimension of the graph of fractional Brownian motion with $H \geq 1/2$