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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.

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
42C15 General harmonic expansions, frames
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