Multivariate FMRAs and FMRA frame wavelets for reducing subspaces of $L^{2}(\mathbb{R}^{d})$

Zhou, Feng-Ying; Li, Yun-Zhang

Multivariate FMRAs and FMRA frame wavelets for reducing subspaces of

$L^{2}(\mathbb{R}^{d})$

Zhou, Feng-Ying ; Li, Yun-Zhang

Kyoto J. Math., Tome 50 (2010) no. 2, p. 83-99 / Harvested from Project Euclid

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Résumé

This article addresses frame multiresolution analyses (FMRAs) and FMRA frame wavelets in the setting of reducing subspaces of

$L^{2}(\mathbb{R}^{d})$ . 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

$|\det M|=2$ , 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

$L^{2}(\mathbb{R}^{d})$ .

Publié le : 2010-05-15
Classification: 42C40

@article{1271187740,
     author = {Zhou, Feng-Ying and Li, Yun-Zhang},
     title = {Multivariate FMRAs and FMRA frame wavelets for reducing subspaces of $L^{2}(\mathbb{R}^{d})$},
     journal = {Kyoto J. Math.},
     volume = {50},
     number = {2},
     year = {2010},
     pages = { 83-99},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1271187740}
}

Zhou, Feng-Ying; Li, Yun-Zhang. Multivariate FMRAs and FMRA frame wavelets for reducing subspaces of $L^{2}(\mathbb{R}^{d})$. Kyoto J. Math., Tome 50 (2010) no. 2, pp.  83-99. http://gdmltest.u-ga.fr/item/1271187740/