Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4605657 | Applied and Computational Harmonic Analysis | 2007 | 19 Pages |
Abstract
For a finite but arbitrary precision, we construct efficient low separation rank representations for the Poisson kernel and for the projector on the divergence free functions in the dimension d=3. Our construction requires computing only one-dimensional integrals. We use scaling functions of multiwavelet bases, thus making these representations available for a variety of multiresolution algorithms. Besides having many applications, these two operators serve as examples of weakly singular and singular operators for which our approach is applicable. Our approach provides a practical implementation of separated representations of a class of weakly singular and singular operators in dimensions dâ©ľ2.
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