论文标题
左翻译和倾斜二元组在海森伯格集团上
Systems of Left Translates and Oblique Duals on the Heisenberg Group
论文作者
论文摘要
在本文中，我们表征左的系统，翻译为$ \ {（2k，l，m）} g：k，l，m \ in \ mathbb {z} \} $，$ g \ in l^2（\ mathbb {h} $ g^λ$。在这里，$（\ mathbb {h} $表示Heisenberg group和$ g^λ$相对于中心变量，$ g $的逆傅立叶变换。这种类型的表征\ emph {riesz}序列的表征使我们能够找到一些具体的示例。我们还研究了左图的结构。 $ \ {l _ {（2k，l，m）} g：k，l，m \ in \ mathbb {z} \} $ on $（\ mathbb {h} $。也用一个示例说明了此结果。
In this paper, we characterize the system of left translates $\{L_{(2k,l,m)}g:k,l,m\in\mathbb{Z}\}$, $g\in L^2(\mathbb{H})$, to be a frame sequence or a \emph{Riesz} sequence in terms of the twisted translates of the corresponding function $g^λ$. Here, $(\mathbb{H}$ denotes the Heisenberg group and $g^λ$ the inverse Fourier transform of $g$ with respect to the central variable. This type of characterization for a \emph{Riesz} sequence allows us to find some concrete examples. We also study the structure of the oblique dual of the system of left translates $\{L_{(2k,l,m)}g:k,l,m\in\mathbb{Z}\}$ on $(\mathbb{H}$. This result is also illustrated with an example.
