The Structure of Finitely Generated Shift-Invariant Subspaces in Super Hilbert Spaces

Author： Zhang Qingyue   Sun Wenchang  

Publisher： Taylor & Francis Ltd

ISSN： 0163-0563

Source： Numerical Functional Analysis and Optimization, Vol.34, Iss.3, 2013-03, pp. : 349-364

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Abstract

We study the structure of finitely generated shift-invariant subspaces with generators from the super Hilbert space L 2(ℜ d )(N). We give a characterization for these subspaces. Moreover, we show that every finitely generated shift-invariant subspace possesses a tight frame. We also give a necessary and sufficient condition for such a space to be principal. Our results generalize similar ones for which generators are from L 2(ℜ d ).

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