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On divergence-free wavelets

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Abstract

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.

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Authors and Affiliations

  1. RWTH Aachen, Institut für Geometrie und Praktische Mathematik, Templergraben 55, D-52056, Aachen, Germany

    Karsten Urban

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  1. Karsten Urban
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Work supported by the Deutsche Forschungsgemeinschaft in the Graduiertenkolleg “Analyse und Konstruktion in der Mathematik” at the RWTH Aachen.

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Urban, K. On divergence-free wavelets. Adv Comput Math 4, 51–81 (1995). https://doi.org/10.1007/BF02123473

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