Divergence-free Wavelet Bases on the Hypercube
نویسنده
چکیده
Abstract. Given a biorthogonal pair of multi-resolution analyses on the interval, by integration or differentiation, we build a new biorthogonal pair of multiresolution 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 [Rev. Mat. Iberoamericana, 8 (1992), pp. 221–237] by P.G. Lemarié-Rieusset for stationary multi-resolution analyses on R. It turns out that it requires a specific choice of boundary conditions.
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