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2012/2013 A Construction of Multiwavelet Sets in the Euclidean Plane
Shiva Mittal
Real Anal. Exchange 38(1): 17-32 (2012/2013).


For \(A=\left( \begin{array}[pos]{ clrr} 0 & 1 \\ a & 0 \end{array} \right),\) where \(a\) is an integer such that \(|a|>1\) and a natural number \(d\) satisfying \(L=(|a|-1)d,\) we obtain that the product \(W\times Q\) of a measurable set \(W\) of the Lebesgue measure \(2\pi L,\) and a measurable set \(Q\) in \(\mathbb R\) such that \(Q\subset aQ,\) is an MRA \(A\)-multiwavelet set of order \(Ld\) in \(\mathbb R^2\) if and only if \(W\) is an \(a\)-multiwavelet set of order \(L\) and \(Q\) is an \(a\)-multiscaling set of order \(d\) associated with \(W.\)


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Shiva Mittal. "A Construction of Multiwavelet Sets in the Euclidean Plane." Real Anal. Exchange 38 (1) 17 - 32, 2012/2013.


Published: 2012/2013
First available in Project Euclid: 29 April 2013

zbMATH: 1276.42024
MathSciNet: MR3083196

Primary: 42C15 , ‎42C40
Secondary: 26A05

Keywords: generalized scaling sets , MSF multiwavelets , multiresolution analysis of multiplicity \(d\) , multiscaling sets , multiwavelet sets , multiwavelets

Rights: Copyright © 2012 Michigan State University Press

Vol.38 • No. 1 • 2012/2013
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