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Orthogonal multiwavelet frames in $$L^2(\mathbb{R}^d)$$. (English) Zbl 1235.42036
Summary: 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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