Wandering r-tuples for unitary systems
Wandering r-tuples for unitary systems
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DOI：
10.1016/j.jmaa.2010.08.059
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发表时间：
2011-02
影响因子：
1.3
通讯作者：
Xunxiang Guo
中科院分区：
文献类型：
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作者：
Xunxiang Guo
研究了作用在Hilbert空间上的酉算子系统U的所有完全游荡r-元组的集合Wr（U）的性质，将Wr（U）用一个固定的游荡r-元组λ和在λ处与U局部交换的所有酉算子的集合参数化.最令人感兴趣的特殊情况是作用在L2（R）上的伸缩（乘2）和平移（乘1）酉算子的系统T_D，T_T，其中完全游荡r-元组恰好是重数为r的正交多小波。并给出了一些应用实例。
The properties of the set Wr(U) of all complete wandering r-tuples for a system U of unitary operators acting on a Hilbert space are investigated by parameterizing Wr(U) in terms of a fixed wandering r-tuple Ψ and the set of all unitary operators which locally commute with U at Ψ. The special case of greatest interest is the system 〈D,T〉 of dilation (by 2) and translation (by 1) unitary operators acting on L2(R), for which the complete wandering r-tuples are precisely the orthogonal multiwavelets with multiplicity r. We also give some examples for its application.