J. Gabardo

activity

20132020

most citedOpen set condition and pseudo Hausdorff measure of self-affine IFSs

7 citations · 8 across the 8 of their papers we have counts for

collaborators

8 papers

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.MG2019★ 7 cited

Open set condition and pseudo Hausdorff measure of self-affine IFSs

Xiaoye Fu, Jean-Pierre Gabardo, Hua Qiu

Let $A$ be an $n \times n$ real expanding matrix and $D$ be a finite subset of $R^{n}$ with $0 \in D$ . The family of maps $\{f_d(x)=A^{-1}(x+d)\}_{d\in\math…

math.FA2016★ 1 cited

Beurling densities and frames of exponentials on the union of small balls

Jean-Pierre Gabardo, Chun-Kit Lai

If $x_{1}, \dots, x_{m}$ are finitely many points in $R^{d}$ , let $E_{ε} = \cup_{i = 1}^{m} x_{i} + Q_{ε}$ , where $Q_{ε} = {x \in R^{d}, ∣ x_{i} ∣ \leq ε /2, i = 1, ..., d}$ and let $f^$ de…

math.FA2014

Gabor orthonormal bases generated by the unit cubes

Jean-Pierre Gabardo, Chun-Kit Lai, Yang Wang

We consider the problem in determining the countable sets $Λ$ in the time-frequency plane such that the Gabor system generated by the time-frequency shifts of the window $χ_{[0,1]^…

math.FA2014

Decomposition of Integral Self-Affine Multi-Tiles

Xiaoye Fu, Jean-Pierre Gabardo

In this paper, we propose a method to decompose an integral self-affine $Z^{n}$ -tiling set $K$ into measure disjoint pieces $K_{j}$ satisfying $K = ⋃ K_{j}$ in…

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.FA2013

Measure of Self-Affine Sets and Associated Densities

Xiaoye Fu, Jean-Pierre Gabardo

Let $B$ be an $n \times n$ real expanding matrix and $D$ be a finite subset of $R^{n}$ with $0 \in D$ . The self-affine set $K = K (B, D)$ is the uniqu…

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…

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

Open set condition and pseudo Hausdorff measure of self-affine IFSs

Beurling densities and frames of exponentials on the union of small balls

Gabor orthonormal bases generated by the unit cubes

Decomposition of Integral Self-Affine Multi-Tiles

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

Measure of Self-Affine Sets and Associated Densities

Frames of multi-windowed exponentials on subsets of Rd

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