These operators are very important inmathematics and physics. They allow the development of generalized wavelets from generalized continuous classical wavelet analysis. Moreover, we have proved in [2] that the generalized two-scale equation associated with the Dunkl operator has a solution and then we can define continuous multiresolution analysis. Dunkl has proved in [1] that there exists a un...

We use the concept of multiresolution analysis and orthonormal basis of wavelet functions to construct an estimator for an unknown density in a given Sobolev’s space. We show consistency with the rate of convergence equal to the optimal minimax rate of convergence. We also discuss some of the features of this new method of estimation on a numerical example.

We introduce here a new method for the numerical resolution of the Vlasov equation on a phase space grid using an adaptive semi-Lagrangian method. The adaptivity is obtained through a multiresolution analysis which enables to keep or remove grid points from the simulation depending on the size of their associated coefficients in a multiresolution expansion. The adaptive algorithm consists in th...

A procedure is proposed for the comparison of molecules. It is based on graph representations of electron density maps smoothed using three different methods: simulation of an X-ray diffraction experiment, wavelet-based multiresolution analysis, and analytical smoothing. Graph representations are obtained using a critical point analysis method. Multiple comparisons between the critical point gr...