Factoring Wavelet Transforms into Lifting Steps.
Finite Orthogonal Transforms and Multireolution Analyses on Intervals.
Finite-Dimensional Approximation of the Inverse Frame Operator.
Fonctions d'échelle interpolantes, polynômes de Bernstein et ondelettes non stationnaires.
The theory of convergence for (non-stationary) scaling functions and the approximation of interpolating scaling filters by means of Bernstein polynomials, allow us to construct a non-stationary interpolating scaling function with interesting approximation properties.
Fractal Wavelet Dimensions and Time Evolution
Fractals and hidden symmetries in DNA.
Frame Analysis of Irregular Periodic Sampling of Signals anf Their Derivatives.
Frames associated with expansive matrix dilations.
We construct wavelet-type frames associated with the expansive matrix dilation on the Anisotropic Triebel-Lizorkin spaces. We also show the a.e. convergence of the frame expansion which includes multi-wavelet expansion as a special case.
Function spaces on the snowflake
We consider two types of Besov spaces on the closed snowflake, defined by traces and with the help of the homeomorphic map from the interval [0,3]. We compare these spaces and characterize them in terms of Daubechies wavelets.
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.
Haar Type Orthonomal Wavelet Bases in R2.
Haar wavelets on the Lebesgue spaces of local fields of positive characteristic
We construct the Haar wavelets on a local field K of positive characteristic and show that the Haar wavelet system forms an unconditional basis for , 1 < p < ∞. We also prove that this system, normalized in , is a democratic basis of . This also proves that the Haar system is a greedy basis of for 1 < p < ∞.