论文标题
Adeles上Gabor框架的变形和低位定理
Deformations and Balian-Low theorems for Gabor frames on the adeles
论文作者
论文摘要
我们将Feichtinger和Kaiblinger的定理概括为统一Gabor框架的线性变形，以设置本地紧凑的Abelian Group $ G $。更确切地说，我们表明，在Feichtinger代数中，$ g $的时频平面上的Gabor框架稳定在晶格的小变形下，这是$ g \ times \ times \ times \ times \ widehat {g} $稳定的。我们在自动形态上使用的拓扑是Braconnier拓扑。我们表征了Feichtinger代数的balian-low定理的群体，准确地保持具有非伴随身份分量的组。这将kaniuth和kutyniok的定理推广到Zak局部紧凑的Abelian群体上的零。我们将结果应用于一类数字理论组，包括与全球领域相关的Adele组。
We generalize Feichtinger and Kaiblinger's theorem on linear deformations of uniform Gabor frames to the setting of a locally compact abelian group $G$. More precisely, we show that Gabor frames over lattices in the time-frequency plane of $G$ with windows in the Feichtinger algebra are stable under small deformations of the lattice by an automorphism of $G \times \widehat{G}$. The topology we use on the automorphisms is the Braconnier topology. We characterize the groups in which the Balian--Low theorem for the Feichtinger algebra holds as exactly the groups with noncompact identity component. This generalizes a theorem of Kaniuth and Kutyniok on the zeros of the Zak transform on locally compact abelian groups. We apply our results to a class of number-theoretic groups, including the adele group associated to a global field.
