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On the equivalence of brushlet and wavelet bases☆

Lasse Borup - No affiliation found

2005/09/01 Full-length article DOI: 10.1016/j.jmaa.2004.12.016 Journal: Journal of Mathematical Analysis and Applications

Abstract:

AbstractWe prove that the Meyer wavelet basis and a class of brushlet systems associated with exponential type partitions of the frequency axis form a family of equivalent (unconditional) bases for the Besov and Triebel–Lizorkin function spaces. This equivalence is then used to obtain new results on nonlinear approximation with brushlets in Triebel–Lizorkin spaces.