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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References


S.T.Ali ,J.P.Antonine ,J.P.Gazean . Wavwlets and their generalization , Springer-Verlag ,New York, 2000 .

D. Bernier and K.F.Taylor . Wavelets from square –integrable representations ,SIAM.Math .Anal ., 27(2) :594-608 ,1996.

D. Bernier and K.F.Taylor . Extensions of the Heisenberg group and wavelet analysis in the plane , Amer.Math.Soc ., 18:217-225 ,1999.

E .Crdero .F.De Mari ,K.Nowak , A .Tabacco . Reproducing subgroups for the metaplectic representation Operator Theory ,Vol .164,227-244 , 2006 .

E .Crdero .F.De Mari ,K.Nowak , A .Tabacco . Analytic feature of reproducing groups for the metaplectic representation , J.Fourier Anal .Appl ., 12(2):157-180 , 2006 .

F.De Mari ,K.Nowak . Analysis of the affine transformations of the time-frequency plane , Math . Soc ., 63(2) :195-218 , 2001 .

G.B . Folland . Harmonic Analysis in Phase Space , Princeton University Press , 1998.

K.Grochenig . Foundations of Time-Frequency Analysis , Birkhauser , Boston , 2001 .

R.S.Laugesen , N.Weaver , G.L.Weiss , and E.N.Wilsson . A characterization of the higher dimensional groups associated with continuous wavelets , Geom .Anal , 12(1) : 89-102 , 2002 .

E . Cordero , F . Damai , K . Nowak , and A. Tabacco . Dimensional Upper Bounds for A dmissible Subgroups for the Metapletic Representation , Italy , 2010 .


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