Abstract
The rise of wavelet analysis in applied mathematics is due to its app-lications and the flexibility. In this article, the notion of biorthogonal two-directional compactly supported trivariate wavelet wraps with poly-scale is developed. Their properties are investigated by algebra theory, means of time-frequency analysis method and, operator theory. An approach for designing a sort of affine triariate dual frames in three-dimensional space is presented. The direct decomposition relationship is provided. In the final, new Riesz bases of space L 2(R 3) are constructed from these wavelet packets. Moreover, it is shown how to draw new Riesz bases of space L 2(R 3, C v ) from these wavelet wraps.
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