Abstract
The rise of wavelet analysis in applied mathematics is due to its applications and the flexibility. In this article, the notion of orthogonal nonseparable four-dimensional wavelet packets, which is the generalization of orthogonal univariate wavelet packets, is introduced. An approach for designing a sort of biorthogonal vector-valued wavelet wraps in three-dimensional space is presented and their biorthogonality traits are characterized by virtue of iteration method and time-frequency representation method. The biorthogonality formulas concerning the-se wavelet wraps are established. Moreover, it is shown how to draw new Riesz bases of space L 2(R 4) from these wavelet wraps. The quarternary dual frames ia also discussed.
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Gao, H., Liu, R. (2011). The Intelligent Algorithm of the Biorthogonal Quarternary Wavelet Packs and Applications in Physics. In: Lin, S., Huang, X. (eds) Advanced Research on Computer Education, Simulation and Modeling. CESM 2011. Communications in Computer and Information Science, vol 175. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21783-8_9
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DOI: https://doi.org/10.1007/978-3-642-21783-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21782-1
Online ISBN: 978-3-642-21783-8
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