NOTES ON MULTIVARIATE PRE-WAVELET DECOMPOSITION

Kuei-Fang Chang

doi:10.11650/twjm/1500406895

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Home > Journals > Taiwanese J. Math. > Volume 2 > Issue 1 > Article

1998 NOTES ON MULTIVARIATE PRE-WAVELET DECOMPOSITION

Kuei-Fang Chang

Taiwanese J. Math. 2(1): 69-85 (1998). DOI: 10.11650/twjm/1500406895

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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.