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

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Showing 2013Show all

4 papers · 1 filter

math.FA2013

Spectral measures associated with the factorization of the Lebesgue measure on a set via convolution

Jean-Pierre Gabardo, Chun-Kit Lai

Let $Q$ be a fundamental domain of some full-rank lattice in $R^{d}$ and let $μ$ and $ν$ be two positive Borel measures on $R^{d}$ such that the convolution $μ * ν$ is a…

math.CO2013★ 1 cited

Classification of tile digit sets as product-forms

Chun-Kit Lai, Ka-Sing Lau, Hui Rao

Let $A$ be an expanding matrix on $R^{s}$ with integral entries. A fundamental question in the fractal tiling theory is to understand the structure of the digit set ${\mathcal…

math.FA2013

Frames of multi-windowed exponentials on subsets of $R^{d}$

Jean-Pierre Gabardo, Chun-Kit Lai

Given discrete subsets $Λ_{j} \subset R^{d}$ , $j = 1, ..., q$ , consider the set of windowed exponentials $⋃_{j = 1}^{q} {g_{j} (x) e^{2 π i < λ, x >} : λ \in Λ_{j}}$ on $L^{2} (Ω)$ . We show that…

math.FA2013★ 34 cited

Some reductions of the spectral set conjecture to integers

Dorin Ervin Dutkay, Chun-Kit Lai

The spectral set conjecture, also known as the Fuglede conjecture, asserts that every bounded spectral set is a tile and vice versa. While this conjecture remains open on ${\mathbb…

Spectral measures associated with the factorization of the Lebesgue measure on a set via convolution

Classification of tile digit sets as product-forms

Frames of multi-windowed exponentials on subsets of Rd

Some reductions of the spectral set conjecture to integers

Frames of multi-windowed exponentials on subsets of $R^{d}$