Homogeneous approximation property for continuous wavelet transforms

Authors:
Bei Liu;Wenchang Sun
Affiliations:
Department of Mathematics, Nankai University, Tianjin 300071, China and LPMC, Nankai University, Tianjin 300071, China;Department of Mathematics, Nankai University, Tianjin 300071, China and LPMC, Nankai University, Tianjin 300071, China
Venue:
Journal of Approximation Theory
Year:
2008

Citing 4
Cited 0

Continuous and discrete wavelet transforms

SIAM Review
Ten lectures on wavelets

Ten lectures on wavelets
Two Banach spaces of atoms for stable wavelet frame expansions

Journal of Approximation Theory
The Homogeneous Approximation Property for wavelet frames

Journal of Approximation Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

The homogeneous approximation property (HAP) for frames is useful in practice and has been developed recently. In this paper, we study the HAP for the continuous wavelet transform. We show that every pair of admissible wavelets possesses the HAP in L^2 sense, while it is not true in general whenever pointwise convergence is considered. We give necessary and sufficient conditions for the pointwise HAP to hold, which depends on both wavelets and functions to be reconstructed.