Multi-frame vectors for unitary systems |
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Authors: | Xunxiang Guo |
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Institution: | 1.Department of Mathematics,Southwestern University of Finance and Economics,Chengdu,Peoples’ Republic of China |
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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 (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. |
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Keywords: | |
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