Protective multi-resolution analyses for L 2 (ℝ 2)

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
Appears in Collections:	Staff Publications

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