Shift reducing subspaces and irreducible-invariant subspaces generated by wandering vectors and applications

Carlos S. Kubrusly and Nhan Levan

Mathematics and Computers in Simulation (MATCOM), 2004, vol. 65, issue 6, 607-627

Abstract: We introduce the notions of elementary reducing subspaces and elementary irreducible-invariant subspaces—generated from wandering vectors—of a shift operator of countably infinite multiplicity, defined on a separable Hilbert space H. Necessary and sufficient conditions for a set of shift wandering vectors to span a wandering subspace are obtained. These lead to characterizations of shift reducing subspaces and shift irreducible-invariant subspaces, as well as a new decomposition of H into orthogonal sum of elementary reducing subspaces. Applications of elementary reducing subspaces to wavelet expansion, and of elementary irreducible-invariant subspaces to wavelet multiresolution analysis (MRA) will be discussed.

Keywords: Wavelet; Scale and time-shift details; Shift-wandering subspace decomposition; Shift reducing subspaces decomposition (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:65:y:2004:i:6:p:607-627

DOI: 10.1016/j.matcom.2004.02.010

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