Abstract
Wavelet analysishas been a powerful tool for exploring and solving many complicated problems in natural science and enginee-ring computation. In this work, the notion of orthogonal matrix-valued trivariate small-wave wraps and wavelet frame wraps, which are generalization of univariate small-wave wraps, is introduced. A new procedure for constructing these vector trivariate small-wave wraps is presented. Their characteristics are studied by using time-frequency analysis method, Banach space theory and finite group theory. Orthogonal formulas concerning the wavelet packs are established. The biorthogonality formulas concerning these wavelet wraps are established. Moreover, it is shown how to draw new Riesz bases of space from these wavelet wraps.
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