交换代数上的可容许向量与迹
Admissible vectors and traces on the commuting algebra
摘要：
给出了一个单模局部紧群的表示，利用交换代数讨论了关联相干态展开的判据。事实证明，对于那些表示，承认这样的扩展，存在唯一的有限迹的交换代数，使容许向量正是迹向量。这个观察是直接从群希尔伯特代数及其相关迹的定义。迹准则允许根据正则表示的中心分解来讨论容许性。特别是，我们提出了一个新的证明的可受理性标准的类型I的情况下。此外，我们推导出的容许准则，推广Weyl-Heisenberg框架的Wexler-Raz双正交关系特征的对偶窗口。
英文摘要：
Given a representation of a unimodular locally compact group, we discuss criteria for associated coherent state expansions in terms of the commuting algebra. It turns out that for those representations that admit such expansions there exists a unique finite trace on the commuting algebra such that the admissible vectors are precisely the tracial vectors for that trace. This observation is immediate from the definition of the group Hilbert algebra and its associated trace. The trace criterion allows to discuss admissibility in terms of the central decomposition of the regular representation. In particular, we present a new proof of the admissibility criteria derived for the type I case. In addition we derive admissibility criteria which generalize the Wexler-Raz biorthogonality relations characterizing dual windows for Weyl-Heisenberg frames.
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