Wavelets and Frequency Decomposition Multilevel Methods
R. Schneider · Notes on numerical fluid mechanics · 1994
An additive decomposition of L 2(Ω) is defined through a suitable bases. The definition of such a basis and the transformation between the bases is performed by a cascade type algorithm using the prolongations of frequency decomposition multigrid methods. If this basis is an unconditional Schauder basis in L 2(Ω) it shares the main properties with wavelets. Particularly, it is, up to a renormalization, also an unconditional basis in a wide scale of Besov- and Triebel-Lizorkin spaces. Such a basis is appropriate for a good approximation of functions with local singularities. For Petrov Galerkin schemes for pseudodifferential equations or singular integral equations this basis gives rise to sparse representations.