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DUAL-SHIFT DECOMPOSITION AND WAVELETS

NHAN LEVAN

Department of Electrical Engineering, University of California in Los Angeles, Los Angeles, CA 90024-1594, USA

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and

CARLOS S. KUBRUSLY

Catholic University of Rio de Janeiro, 22453-900, Rio de Janeiro, RJ, Brazil

Corresponding author.

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https://doi.org/10.1142/S0219691314500143Cited by:0 (Source: Crossref)

Abstract

We introduce the notion of dual-shift decomposition of an arbitrary Hilbert space, which is given in terms of two unilateral shifts. After ensuring conditions for the existence of it, such a decomposition is then constructed for the concrete space ℒ²[0, 1], on which the two unilateral shifts are parts of the dilation-by-2 and the translation-by-1 on ℒ²(ℝ). Using multiresolution analysis (MRA) of wavelet theory it is shown the existence of a Haar-system-type orthonormal basis for ℒ²[0, 1], which is combined with the dual-shift decomposition to yield a refined decomposition for ℒ²[0, 1].

Preliminary results of this paper were presented at SOTA2 Conference held in Rio in 2001.

Keywords:

AMSC: 42C40, 47A15

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