On the Nonexistence of Certain Divergence-free Multiwavelets
We show that there are no biorthogonal pairs of divergence-free multiwavelet families on Rnhaving any regularity, such that both biorthogonal families have compactly supported, divergence-free generators. This main result generalizes Lemarié’s bivariate result. In particular, our method is based on vector-valued multiresolution analyses.
KeywordsCompact Support Trigonometric Polynomial Multiresolution Analysis Riesz Basis Dyadic Cube
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