Summary
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.
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Schneider, R. (1994). Wavelets and Frequency Decomposition Multilevel Methods. In: Hackbusch, W., Wittum, G. (eds) Adaptive Methods — Algorithms, Theory and Applications. Notes on Numerical Fluid Mechanics (NNFM). Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14246-1_18
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DOI: https://doi.org/10.1007/978-3-663-14246-1_18
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