Homogeneous approximation property for wavelet frames with matrix dilations
✍ Scribed by Wenchang Sun
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 201 KB
- Volume
- 283
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
The homogeneous approximation property (HAP) for wavelet frames was studied recently. The HAP is useful in practice since it means that the number of building blocks involved in a reconstruction of a function up to some error is essentially invariant under time‐scale shifts. In this paper, we prove the HAP for wavelet frames generated by admissible wavelet functions with arbitrary translation parameters and a class of dilation matrices. Moreover, we show that the approximation is uniform to some extent whenever wavelet functions satisfy moderate smooth and decaying conditions (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)