Lasse Borup

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In this paper we study nonlinear approximation and data representation with redundant function dictionaries. In particular, approximationwith redundant wavelet bi-frame systems is studied in detail. Several results for orthonormal wavelets are generalized to the redundant case. In general, for a wavelet bi-frame system the approximation properties are(More)
We study tight wavelet frame systems in Lp(R), and prove that such systems (under mild hypotheses) give atomic decompositions of L p(R) for 1 < p < . We also characterize Lp(R) and Sobolev space norms by the analysis coefficients for the frame. We consider Jackson inequalities for best mterm approximation with the systems in Lp(R) and prove that such(More)
A construction of Triebel-Lizorkin type spaces associated with flexible decompositions of the frequency space R is considered. The class of admissible frequency decompositions is generated by a one parameter group of (anisotropic) dilations on R and a suitable decomposition function. The decomposition function governs the structure of the decomposition of(More)
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