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Spring 2010 Multivariate FMRAs and FMRA frame wavelets for reducing subspaces of L2(Rd)
Feng-Ying Zhou, Yun-Zhang Li
Kyoto J. Math. 50(1): 83-99 (Spring 2010). DOI: 10.1215/0023608X-2009-006


This article addresses frame multiresolution analyses (FMRAs) and FMRA frame wavelets in the setting of reducing subspaces of L2(Rd). For a general expansive matrix, we obtain a characterization and some conditions for a frame-scaling function to generate an FMRA, and we prove that an arbitrary reducing subspace must admit an FMRA. For an expansive matrix M with |detM|=2, we establish a sufficient and necessary condition for FMRAs to admit a single FMRA frame wavelet, give an explicit construction of FMRA frame wavelets, and study the relation between s-frame wavelets and FMRA frame wavelets. These results are also new in the setting of L2(Rd).


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Feng-Ying Zhou. Yun-Zhang Li. "Multivariate FMRAs and FMRA frame wavelets for reducing subspaces of L2(Rd)." Kyoto J. Math. 50 (1) 83 - 99, Spring 2010.


Published: Spring 2010
First available in Project Euclid: 13 April 2010

zbMATH: 1228.42044
MathSciNet: MR2629644
Digital Object Identifier: 10.1215/0023608X-2009-006

Primary: ‎42C40

Rights: Copyright © 2010 Kyoto University


Vol.50 • No. 1 • Spring 2010
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