New bases for Triebel-Lizorkin and Besov spaces |
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Authors: | G Kyriazis P Petrushev |
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Institution: | Department of Mathematics and Statistics, University of Cyprus, P. O. Box 20537, 1678 Nicosia, Cyprus ; Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208 |
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Abstract: | We give a new method for construction of unconditional bases for general classes of Triebel-Lizorkin and Besov spaces. These include the , , potential, and Sobolev spaces. The main feature of our method is that the character of the basis functions can be prescribed in a very general way. In particular, if is any sufficiently smooth and rapidly decaying function, then our method constructs a basis whose elements are linear combinations of a fixed (small) number of shifts and dilates of the single function . Typical examples of such 's are the rational function and the Gaussian function This paper also shows how the new bases can be utilized in nonlinear approximation. |
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Keywords: | Triebel-Lizorkin spaces Besov spaces unconditional bases nonlinear approximation wavelets |
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