2002/09/19 by Hartmut Fuehr, Fuehr, Hartmut · 2 citations
Mathematics · Physics and Astronomy · #43A32 #46K15 #81R30 #Advanced Algebra and Geometry #FOS: Mathematics #FOS: Physical sciences #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #math-ph #math.MP #math.OA #msc:43A32 #msc:46K15 #msc:81R30
paper · pdf · doi:10.48550/arxiv.math/0209245
8 pages
arxiv created 2002/09/19 · openalex publication_date 2002/09/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.