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2009/2010 Wavelet Sets Accumulating at the Origin
Rajeshwari Dubey, Aparna Vyas
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Real Anal. Exchange 35(2): 463-478 (2009/2010).


For a natural number $n$, selecting a $2n$-interval symmetric wavelet set by making use of a result of Arcozzi, Behera and Madan [J. Geom. Anal. 13 (2003), 557-579], we construct a family of symmetric wavelet sets accumulating at the origin. Such a family of wavelet sets is also obtained from a family of symmetric six-interval wavelet sets provided by them in the same paper. Three-interval wavelet sets are employed in having a family of wavelet sets accumulating at the origin which are non-symmetric. Further, we obtain a larger class of $H^{2}$-wavelet sets accumulating at the origin, which include the one given by Behera in [Bull. Polish Acad. Sci. Math. 52 (2004), 169-178]. Finally, non-MSF non-MRA wavelets are obtained through the selected family of $2n$-interval symmetric wavelet sets.


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Rajeshwari Dubey. Aparna Vyas. "Wavelet Sets Accumulating at the Origin." Real Anal. Exchange 35 (2) 463 - 478, 2009/2010.


Published: 2009/2010
First available in Project Euclid: 22 September 2010

zbMATH: 1268.42064
MathSciNet: MR2683611

Primary: 42C15 , ‎42C40

Keywords: dilation equivalence , dimension function , MSF wavelets , translation equivalence , wavelet set , Wavelets

Rights: Copyright © 2009 Michigan State University Press

Vol.35 • No. 2 • 2009/2010
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