Wavelets generated by layer potentials.
By means of the limit and jump relations of classical potential theory in \(\mathbb{R}^3\), a wavelet theory on a regular surface (like sphere or ellipsoid) is established. The authors use the kernels of the layer potentials to introduce new wavelets on regular surfaces. The multiresolution analysis (i.e., scaling functions, scale spaces, wavelets, detail spaces) is defined. A pyramid scheme (tree algorithm) for fast computation is given. The performance of this wavelet framework is illustrated by the zoom-in property, the detection of a high frequency perturbation and the data compression. Finally, a fast multiscale representation of the solution of exterior Dirichlet and Neumann boundary value problems is given.
scientific article; zbMATH DE number 1957121