Abstract
Wavelet analysis has become an active research field for over twenty years. In this work, we develop the concept of a class of biorthogonal vector-valued multivariate wavelet packets associated with a pair of biorthogonal scaling function vector. A new method for constructing biorthogonal multivariate vector wavelet packets is formulated. Their characteristics are researched by means of operator theory, time frequency analysis method and matrix theory. Three orthogonality formulas regarding the wavelet packets are provided. Birthogonality decomposition relation formulas of the space L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> are obtained by constructing a series of subspaces of the vector-valued wavelet packets. Furthermore, several wavelet packet bases of space L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> are constructed from the wavelet packets.
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