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On divergence-free wavelets. (English) Zbl 0822.42020
Summary: This paper is concerned with the construction of compactly supported divergence-free vector wavelets. Our construction is based on a large class of refinable functions which generate multivariate multiresolution analyses which includes, in particular, the non tensor product case.
For this purpose, we develop a certain relationship between partial derivatives of refinable functions and wavelets with modifications of the coefficients in their refinement equation. In addition, we demonstrate that the wavelets we construct form a Riesz basis for the space of divergence-free vector fields.

MSC:
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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