Wavelet Transforms for Semidirect Product Groups with Not Necessarily Commutative Normal Subgroups
Wavelet Transforms for Semidirect Product Groups with Not Necessarily Commutative Normal Subgroups
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DOI：
10.1007/s00041-005-5002-0
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发表时间：
2006-02
影响因子：
1.2
通讯作者：
H. Ishi
中科院分区：
文献类型：
--
作者：
H. Ishi
设G是可分局部紧幺模群N的半直积群，其闭子群H为Aut（N）.群N不一定是交换的。我们考虑G的酉表示在L2（N）上自然实现的不可约子表示，并研究与之相关的小波变换。此外，不可约子空间由N上某些类似于柯西-赛格积分的奇异积分来刻画。
Let G be the semidirect product group of a separable locally compact unimodular group N of type I with a closed subgroup H of Aut(N). The group N is not necessarily commutative. We consider irreducible subrepresentations of the unitary representation of G realized naturally on L2(N), and investigate the wavelet transforms associated to them. Furthermore, the irreducible subspaces are characterized by certain singular integrals on N analogous to the Cauchy-Szegö integral.