Admissible vectors for unitary representations of locally compact groups are the basis for group frame and covariant coherent state expansions. Main tools in the study of admissible vectors have been Plancherel and central integral decompositions, of applicability only under certain separability and semifiniteness restrictions. In this work, we present a study of admissible vectors in terms of convolution Hilbert algebras valid for arbitrary unitary representations of general locally compact groups.

中文翻译：

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容许向量和希尔伯特代数

局部紧凑群的统一表示的可允许向量是群框架和协变相干态展开的基础。研究可允许向量的主要工具是Plancherel和中心积分分解，仅在某些可分离性和半有限性约束下才适用。在这项工作中，我们以卷积希尔伯特代数为基础，对一般局部紧致群的任意unit表示有效的可容许向量的研究。