Gabor Frames, Unimodularity, and Window Decay.
Gabor meets Littlewood-Paley: Gabor expansions in
It is known that Gabor expansions do not converge unconditionally in and that cannot be characterized in terms of the magnitudes of Gabor coefficients. By using a combination of Littlewood-Paley and Gabor theory, we show that can nevertheless be characterized in terms of Gabor expansions, and that the partial sums of Gabor expansions converge in -norm.
G-continuous frames and coorbit spaces.
Generalized Calderón conditions and regular orbit spaces
The construction of generalized continuous wavelet transforms on locally compact abelian groups A from quasi-regular representations of a semidirect product group G = A ⋊ H acting on L²(A) requires the existence of a square-integrable function whose Plancherel transform satisfies a Calderón-type resolution of the identity. The question then arises under what conditions such square-integrable functions exist. The existing literature on this subject leaves a gap between sufficient and necessary criteria....
Generalized Multi-Resolution Analyses and a Construction Procedure for All Wavelet Sets in ...
Gibbs' Phenomenon and Arclength.
Gibbs' Phenomenon for Sampling Series and What To Do About It.
Gibbs Phenomenon on Sampling Series Based on Shannon's and Meyer's Wavelet Analysis.
Good-λ inequalities for wavelets of compact support
For a wavelet ψ of compact support, we define a square function and a maximal function NΛ. We then obtain the equivalence of these functions for 0 < p < ∞. We show this equivalence by using good-λ inequalities.