Abstract
We introduce the Wiener space and then consider wavelets which are not necessarily compactly supported but have a decay condition at innity. Under the Wiener condition, a wavelet and its bi-orthogonal wavelet have the same rate of decay at innity and the same moment. Under a certain sucient condition, we prove the existence of a pre-wavelet basis in the multi-dimensional case. Furthermore, pre-wavelets and their bi-orthogonal pre-wavelets have the same rate of decay at innity and the same number of vanishing moments.
Citation
Kuei-Fang Chang. "NOTES ON MULTIVARIATE PRE-WAVELET DECOMPOSITION." Taiwanese J. Math. 2 (1) 69 - 85, 1998. https://doi.org/10.11650/twjm/1500406895
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