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A construction of multiwavelet sets in the Euclidean plane. (English) Zbl 1276.42024

The paper is devoted to the construction of multiwavelet sets in the Euclidean plane. More precisely, for a \(2\times 2\) matrix \(A\) with the first row vector being \((0\,\,1)\) and the second row vector being \((a\,\,0)\), the author provides a characterization for the product \(W\times Q\) of a measurable set \(W\) of measure \(2\pi (|a|-1)d\) and a measurable set \(Q\) in \(\mathbb R\) such that \(Q\subset aQ\) is an MRA \(A\)-multiwavelet set of order \((|a|-1)d^2\) in \(\mathbb R^2\), where \(a\) is an integer such that \(|a|>1\) and \(d\) is a natural number.

MSC:

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

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