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On the construction of multivariate (pre)wavelets |
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| Authors: | Carl de Boor Ronald A DeVore Amos Ron |
| Institution: | 1. Center for Mathematical Sciences, University of Wisconsin-Madison, 1308 W. Dayton Street, 53706, Madison, Wisconsin, U.S.A. 2. Department of Mathematics, University of South Carolina, 29208, Columbia, South Carolina, U.S.A. 3. Computer Sciences Department, University of Wisconsin-Madison, 1210 W. Dayton Street, 53706, Madison, Wisconsin, U.S.A. |
| Abstract: | A new approach for the construction of wavelets and prewavelets onR d from multiresolution is presented. The method uses only properties of shift-invariant spaces and orthogonal projectors fromL 2(R d ) onto these spaces, and requires neither decay nor stability of the scaling function. Furthermore, this approach allows a simple derivation of previous, as well as new, constructions of wavelets, and leads to a complete resolution of questions concerning the nature of the intersection and the union of a scale of spaces to be used in a multiresolution. |
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