ISSN: 2375-3927
International Journal of Mathematical Analysis and Applications  
Manuscript Information
 
 
Applications on Triagular Subgroups of Sp with Reproducing Groups
International Journal of Mathematical Analysis and Applications
Vol.5 , No. 3, Publication Date: Sep. 3, 2018, Page: 66-84
177 Views Since September 3, 2018, 37 Downloads Since Sep. 3, 2018
 
 
Authors
 
[1]    

Simon Joseph, Department of Mathematics, University of Juba, Juda, South Sudan.

[2]    

Manal Juma, Department of Mathematics, Prince Sattam bin Abdulaziz University, Alkharj, Kingdom of Saudi Arabia.

[3]    

Isra Mukhtar, Department of Mathematics, Shaqra University, Al-Riyadh, Kingdom of Saudi Arabia.

 
Abstract
 

Consider the (extended) metaplectic representation of the semidirect product with being a symmetric matrix and D a close subgroup of , are the main concerned. They shall give a general setting for the reproducibility of such groups which include and assemble the ones for the single examples treated in Cordero et al.(2006) [3]. As a byproduct, the extended metaplectic representation restricted to some classes of such subgroups is either the Schrodinger representation of or the wavelet representation of with closed subgroup of by E. Cordero, A. Tabacco [11]. Finally, we shall provided new examples of reproducing groups of the type in dimension = 1.


Keywords
 

Reproducing Formula, Metaplectic Representation, Wigner Distribution, Semidirect Product


Reference
 
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E. Cordero, F. De Mari, K. Nowak, and A. Tabacco, Analytic features of reproducing groups for the metaplectic representation, J. Fourier Anal. Appl 12 (3) (2006) 157-180.

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E. Cordero, F. DeMari, K. Nowak, A. Tabacco, A dimensional bound for reproducing subgroups of the symplectic group, Mth. Nachr. 283 (7) (2010) 1-12.

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[11]    

E. Cordero, A. Tabacco, Triagular subgroups of Sp(d, ) and reproducing formulae, Journal of Functional Analysis 264 (2013) 2034-2058. http://dx.doi.org/10.1016/j.jfa.2013.02.004





 
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