On divergence-free wavelets |
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Authors: | Karsten Urban |
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Institution: | (1) RWTH Aachen, Institut für Geometrie und Praktische Mathematik, Templergraben 55, D-52056 Aachen, Germany |
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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.Work supported by the Deutsche Forschungsgemeinschaft in the Graduiertenkolleg Analyse und Konstruktion in der Mathematik at the RWTH Aachen. |
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Keywords: | Wavelets divergence-free vector functions |
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