Please use this identifier to cite or link to this item: https://doi.org/10.1007/s00041-004-3065-y
Title: Protective multi-resolution analyses for L 2 (ℝ 2)
Authors: Packer, J.A. 
Rieffel, M.A.
Keywords: Hubert c*-module
K-theory.
Module frames
Multi-resolution
Projective modules
Tight frames
Wavelets
Issue Date: 2004
Citation: Packer, J.A., Rieffel, M.A. (2004). Protective multi-resolution analyses for L 2 (ℝ 2). Journal of Fourier Analysis and Applications 10 (5) : 439-464. ScholarBank@NUS Repository. https://doi.org/10.1007/s00041-004-3065-y
Abstract: We define the notion of "projective" multiresolution analyses, for which, by definition, the initial space corresponds to a finitely generated projective module over the algebra C (∥ n) of continuous complex-valued functions on an n -torus. The case of ordinary multi-wavelets is that in which the projective module is actually free. We discuss the properties of pmjective multiresolution analyses, including the frames which they provide for L 2(ℝ n). Then we show how to construct examples for the case of any diagonal 2×2 dilation matrix with integer entries, with initial module specified to be any fixed finitely generated projective C(T 2)-module. We compute the isomorphism classes of the corresponding wavelet modules. © 2004 birkhäuser boston. All rights reserved.
Source Title: Journal of Fourier Analysis and Applications
URI: http://scholarbank.nus.edu.sg/handle/10635/103984
ISSN: 10695869
DOI: 10.1007/s00041-004-3065-y
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