University of MaraghehSahand Communications in Mathematical Analysis2322-580717320200701On Some Characterization of Generalized Representation Wave-Packet Frames Based on Some Dilation Group931064053110.22130/scma.2019.106144.592ENAtefeRazghandiDepartment of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O.Box 397, Sabzevar, Iran.Ali AkbarArefijamaalDepartment of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O.Box 397, Sabzevar, Iran.0000-0003-2153-352XJournal Article20190412In this paper we consider (extended) metaplectic representation of the semidirect product $G_{\mathbb{J}}=\mathbb{R}^{2d}\times\mathbb{J}$ 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.https://scma.maragheh.ac.ir/article_40531_24c9e8eda66fd4f95602c706a8047474.pdf