### Orthogonal Multiwavelet Frames in ${L}^{2}({R}^{d})$

Liu Zhanwei, Hu Guoen, and Wu Guochang
Source: J. Appl. Math. Volume 2012 (2012), Article ID 846852, 18 pages.

#### Abstract

We characterize the orthogonal frames and orthogonal multiwavelet frames in ${L}^{2}({R}^{d})$ with matrix dilations of the form $(Df)(x)=\sqrt{|\text{d}\text{e}\text{t}A|}f(Ax)$, where $A$ is an arbitrary expanding $d×d$ matrix with integer coefficients. Firstly, through two arbitrarily multiwavelet frames, we give a simple construction of a pair of orthogonal multiwavelet frames. Then, by using the unitary extension principle, we present an algorithm for the construction of arbitrarily many orthogonal multiwavelet tight frames. Finally, we give a general construction algorithm for orthogonal multiwavelet tight frames from a scaling function.

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