MULTI-FRAME VECTORS FOR UNITARY SYSTEMS

作者：Guo Xunxiang^*

来源：Indian Journal of Pure and Applied Mathematics, 2012, 43(4): 391-409.

• Multi-frame vector
• multi-Riesz vector
• complete wandering r-tuple
• local commutant
• unitary system

In this paper, the set of all complete multi-normalized tight frame vectors NFr(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 C-Psi r(U), the set of all operators which locally commute with U at Psi(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.

• 出版日期2012-8
• 单位西南大学