Approximation with wave packets generated by a refinable function

Borup, Lasse; Nielsen, Morten

doi:10.1090/S0002-9939-05-07778-6

Approximation with wave packets generated by a refinable function
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by Lasse Borup and Morten Nielsen PDF

Proc. Amer. Math. Soc. 133 (2005), 2409-2418 Request permission

Abstract:

We consider best $m$-term approximation in $L_p(\mathbb {R}^d)$ with wave packets generated by a single refinable function. The main examples of wave packets are orthonormal wavelets, or more generally wavelet frames based on a multiresolution analysis (so-called framelets). The approximation classes associated with best $m$-term approximation in $L_p(\mathbb {R}^d)$ for a large class of wave packets are completely characterized in terms of Besov spaces. As an application of the main result, we show that for $m$-term approximation in $L_p(\mathbb {R}^d)$ with elements from an oversampled version of a framelet system with compactly supported generators, the associated approximation classes turn out to be (essentially) Besov spaces.

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