On Some Characterization of Generalized Representation Wave-Packet Frames Based on Some Dilation Group
Journal: Sahand Communications in Mathematical Analysis (Vol.17, No. 3)Publication Date: 2020-07-01
Authors : Atefe Razghandi; Ali Akbar Arefijamaal;
Page : 93-106
Keywords : Representation frames; Dilation groups; Dual frames; Continuous frames;
Abstract
In this paper we consider (extended) metaplectic representation of the semidirect product $G_{mathbb{J}}=mathbb{R}^{2d}timesmathbb{J}$ 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.
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