On divergence-free wavelets
- Cite this article as:
- Urban, K. Adv Comput Math (1995) 4: 51. doi:10.1007/BF02123473
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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.