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2014 Contractibility of Simple Scaling Sets
N. K. Shukla, G.C.S. Yadav
Commun. Math. Anal. 16(1): 31-46 (2014).


In this paper, we show that the space of three-interval scaling functions with the induced metric of $L^2(\mathbb R)$ consists of three pathcomponents each of which is contractible and hence, the first fundamental group of these spaces is zero. One method to construct simple scaling sets for $L^2(\mathbb R)$ and $H^2(\mathbb R)$ is described. Further, we obtain a characterization of a method to provide simple scaling sets for higher dimensions with the help of lower dimensional simple scaling sets and discuss scaling sets, wavelet sets and multiwavelet sets for a reducing subspace of $L^2(\mathbb R^n)$. The contractibility of simple scaling sets for different subspaces are also discussed.


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N. K. Shukla. G.C.S. Yadav. "Contractibility of Simple Scaling Sets." Commun. Math. Anal. 16 (1) 31 - 46, 2014.


Published: 2014
First available in Project Euclid: 4 November 2013

zbMATH: 1297.42052
MathSciNet: MR3161734

Primary: ‎42C40

Keywords: contractibility , multiresolution analysis , Pathconnectivity , ‎wavelet , Wavelet and Scaling sets

Rights: Copyright © 2014 Mathematical Research Publishers


Vol.16 • No. 1 • 2014
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