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ISSN 1088-6826(e) ISSN 0002-9939(p)

Approximation with wave packets generated by a refinable function

Author(s): Lasse Borup; Morten Nielsen
Journal: Proc. Amer. Math. Soc. 133 (2005), 2409-2418.
MSC (2000): Primary 41A46; Secondary 41A17, 42C40
Posted: February 25, 2005
MathSciNet review: 2138884
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Abstract: We consider best -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 -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 -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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Additional Information:

Lasse Borup
Affiliation: Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg East, Denmark
Email: lasse@math.auc.dk

Morten Nielsen
Affiliation: Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg East, Denmark
Email: mnielsen@math.auc.dk

DOI: 10.1090/S0002-9939-05-07778-6
PII: S 0002-9939(05)07778-6
Keywords: Refinable functions, nonlinear approximation, framelet systems, Jackson inequality, Bernstein inequality, Besov spaces
Received by editor(s): July 15, 2003
Received by editor(s) in revised form: April 14, 2004
Posted: February 25, 2005
Additional Notes: This work was supported in part by the Danish Technical Science Foundation, Grant no. 9701481
Communicated by: David R. Larson
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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