On Some Characterization of Generalized Representation Wave-Packet Frames Based on Some Dilation Group

In this paper we consider  (extended) metaplectic representation of the  semidirect product  G_{\mathbb{J}}=\mathbb{R}^{۲d}\times\mathbb{J}  where \mathbb{J} is a closed subgroup of Sp(d,\mathbb{R}), the symplectic group. We will investigate continuous representation frame on G_{\mathbb{J}}. We also discuss the existence of duals for such frames and give several characterization for them. Finally, we rewrite the dual conditions, by using the Wigner distribution and obtain more reconstruction formulas.

Keywords:

Representation frames , Dilation groups , Dual frames , Continuous frames