Orthogonal multiwavelet frames in \(L^2(\mathbb{R}^d)\).

*(English)*Zbl 1235.42036Summary: We characterize the orthogonal frames and orthogonal multiwavelet frames in \(L^2(\mathbb{R}^d)\) with matrix dilations of the form \((Df)(x) = \sqrt{|\det A|} f(Ax)\), where \(A\) is an arbitrary expanding \(d \times d\) 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.

##### MSC:

42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |

42C15 | General harmonic expansions, frames |

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\textit{L. Zhanwei} et al., J. Appl. Math. 2012, Article ID 846852, 18 p. (2012; Zbl 1235.42036)

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