论文标题
局部紧凑型组的量子谐波分析
Quantum harmonic analysis on locally compact groups
论文作者
论文摘要
在局部紧凑的组上，我们引入了相位空间表示形式的协变量量化方案和类似物以及混合国家定位运算符。这些概括了Aggine Group和Heisenberg Group的相应概念。该方法基于与局部紧凑的组的正方形集成表示，可集成功能和跟踪类操作员之间的两种类型的汇集。对于非偏离组的情况，这些卷积仅适用于可接受的操作员，这是对仿射组最近指出的可允许小波概念的扩展。
On a locally compact group we introduce covariant quantization schemes and analogs of phase space representations as well as mixed-state localization operators. These generalize corresponding notions for the affine group and the Heisenberg group. The approach is based on associating to a square integrable representation of the locally compact group two types of convolutions between integrable functions and trace class operators. In the case of non-unimodular groups these convolutions only are well-defined for admissible operators, which is an extension of the notion of admissible wavelets as has been pointed out recently in the case of the affine group.
