幂零李群上平移生成系统的再生公式
Reproducing formulas associated to translation generated systems on Nilpotent Lie Groups
摘要：
设$G$是连通、单连通、幂零李群，其不可约酉表示模中心平方可积。我们得到表征结果再现公式与左平移生成系统在$ L^2(G)$。不同于以往对幂零李群上离散框架的研究，本文的研究是在连续框架的基础上进行的，这意味着再生公式是以整表示形式给出的，而不是以离散和形式给出的.作为我们对Heisenberg群的结果的一个推论，得到了与$L^2(\mathbb R^d)$的正交规范Gabor系统有关的再生公式.
英文摘要：
Let $G$ be a connected, simply connected, nilpotent Lie group whose irreducible unitary representations are square-integrable modulo the center. We obtain characterization results for reproducing formulas associated with the left translation generated systems in $ L^2(G)$. Unlike the previous study of discrete frames on the nilpotent Lie groups, the current research occurs within the set up of continuous frames, which means the resulting reproducing formulas are given in terms of integral representations instead of discrete sums. As a consequence of our results for the Heisenberg group, a reproducing formula associated with the orthonormal Gabor systems of $L^2(\mathbb R^d)$ is obtained.
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