Abstract
We consider the (extended) metaplectic representation of the semidirect product G of the symplectic group and the Heisenberg group. By looking at the standard resolution of the identity formula and inspired by previous work [5], [13], [4], we introduce the notion of admissible (reproducing) subgroup of G via the Wigner distribution. We prove some features of admissible groups and then exhibit an explicit example (d = 2) of such a group, in connection with wavelet theory.KeywordsMetaplectic representationsymplectic groupwaveletsWigner distribution
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