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Summer 2010 The path-connectivity of MRA wavelets in $L^2(\mathbb {R}^{d})$
Zhongyan Li, Xingde Dai, Yuanan Diao, Wei Huang
Illinois J. Math. 54(2): 601-620 (Summer 2010). DOI: 10.1215/ijm/1318598674

Abstract

We show that for any $d\times d$ expansive matrix $A$ with integer entries and $|\det(A)|=2$, the set of all $A$-dilation MRA wavelets is path-connected under the $L^2(\mathbb{R}^d)$ norm topology. We do this through the application of $A$-dilation wavelet multipliers, namely measurable functions $f$ with the property that the inverse Fourier transform of $(f\widehat{\psi})$ is an $A$-dilation wavelet for any $A$-dilation wavelet $\psi$ (where $\widehat{\psi}$ is the Fourier transform of $\psi$). In this process, we have completely characterized all $A$-dilation wavelet multipliers for any integral expansive matrix $A$ with $|\det(A)|=2$.

Citation

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Zhongyan Li. Xingde Dai. Yuanan Diao. Wei Huang. "The path-connectivity of MRA wavelets in $L^2(\mathbb {R}^{d})$." Illinois J. Math. 54 (2) 601 - 620, Summer 2010. https://doi.org/10.1215/ijm/1318598674

Information

Published: Summer 2010
First available in Project Euclid: 14 October 2011

zbMATH: 1238.42019
MathSciNet: MR2846475
Digital Object Identifier: 10.1215/ijm/1318598674

Subjects:
Primary: 42-XX , 46-XX

Rights: Copyright © 2010 University of Illinois at Urbana-Champaign

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Vol.54 • No. 2 • Summer 2010
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