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.