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Title of article :
Shift reducing subspaces and irreducible-invariant subspaces generated by wandering vectors and applications Original Research Article
Author/Authors :
Carlos S. Kubrusly، نويسنده , , Nhan Levan، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2004
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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 :
Shift-wandering subspace decomposition , Scale and time-shift details , Shift reducing subspaces decomposition , Wavelet
Journal title :
Mathematics and Computers in Simulation
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Link To Document :