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ShowMe Analysis Meeting 2004 |
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ShowMe Analysis Meeting 2004 |
Abstract: In this talk we will discuss compactly supported wavelet bases for Sobolev spaces. Starting with a pair of compactly supported refinable functions satisfying a very mild condition, we provide a general principle for the construction of stable wavelet bases for Sobolev spaces. Our approach combines both biorthogonal wavelets of Cohen and Daubechies and semi-orthogonal wavelets of Chui and Wang. But the pair of refinable functions in our work are not required to be biorthogonal or semi-orthogonal. The added flexibility allows us to construct wavelets with relatively small supports. We will also discuss various applications of the aforementioned wavelet bases.