Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4605322 | Applied and Computational Harmonic Analysis | 2011 | 19 Pages |
Abstract
Given a biorthogonal pair of multi-resolution analyses on the interval, by integration or differentiation, we build a new biorthogonal pair of multi-resolution analyses. Using both pairs, isotropic or, as we focus on, anisotropic divergence-free wavelet bases on the hypercube are constructed. Our construction generalizes the one from [16] by P.G. Lemarié-Rieusset (1992) for stationary multi-resolution analyses on R. It turns out that it requires a specific choice of boundary conditions.
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