Multi-frame vectors for unitary systems

Xunxiang Guo ()
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Xunxiang Guo: Southwestern University of Finance and Economics

Indian Journal of Pure and Applied Mathematics, 2012, vol. 43, issue 4, 391-409

Abstract: Abstract In this paper, the set of all complete multi-normalized tight frame vectors NF r (U) with multiplicity r and the set of all complete multi-frame vectors F r (U) with multiplicity r for a system U of unitary operators acting on a separable Hilbert space are characterized in terms of co-isometries and surjective operators in $\mathcal{C}_{\Psi ^r } $ (U), the set of all operators which locally commute with U at Ψ r , a fixed complete wandering r-tuple for U. Then we study the linear combinations of multi-frame vectors for U and establish some conditions under which these combinations are still the same type of multi-frame vectors for U. Finally, we establish some interesting properties for multi-frame vectors when U is a unitary group. All these results have potential applications in the theory of multi-Gabor systems and multi-wavelet systems.

Keywords: Multi-frame vector; multi-Riesz vector; complete wandering r-tuple; local commutant; unitary system (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s13226-012-0024-1

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