Verifications on Dimensional Upper Bounds for a Dmissible Subgroups for the Metapletic Representation

Simon Joseph, Murtada Amin, Ahmed Sufyan

Abstract


We prove dimensional upper bounds for admissible Lie subgroups H of  G =  . The notation of admissibility captures natural geometric phenomena of the phase space and it is a sufficient condition for a subgroup to be reproducing  . It is expressed in terms of absolutely convergent integrals of Wigner distributions , translated by the affine action of the subgroup . They showed that dim H  , where as if H  , then dim H  , [10] . Both bounds are shown to be optimal.


Keywords


Metaplectic representation ; reproducing formula; symplectic group; Wavelets; Wigner distribution; semidirect product; Lie group; Lie algebra.

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