LCA群的Landau必要密度条件

关于LCA群上Gabor系统的Riesz对偶

On Riesz duals for the Gabor system on LCA groups

本文研究局部紧阿贝尔群上可分离均匀时频格点中，伴随Gabor系统作为给定Gabor框架的R-对偶的条件，并证明Gabor Bessel序列完备的必要条件。

多镶嵌集、Riesz基和LCA群中临界密度附近的抽样

Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups

本文证明了局部紧交换群G的Paley-Wiener空间在临界密度附近的采样集和插值集的存在性。这解决了Gröchenig，Kutyniok和Seip在文章中留下的问题：“LCA群的Landau密度条件”（J. of Funct. Anal. 255（2008）1831-1850）。为了实现这一结果，我们证明了存在的普遍Riesz基地的特点，L2（Ω），提供了相对紧凑的子集Ω的对偶群G满足一个multi-tiling条件。这最后一个结果推广Fuglede定理，并延伸到LCA组设置最近的建设Riesz基地的指数在有界集的Rd。

Two wavelet multipliers and Landau-Pollak-Slepian operators on locally compact abelian groups associated to right-$H$-translation-invariant functions

By using a coset of closed subgroup, we define a Fourier like transform for locally compact abelian (LCA) topological groups. We studied two wavelet multipliers and Landau-Pollak-Slepian operators on locally compact abelian topological groups associated to the transform and show that the transforms are $L^p$bounded linear operators, and are in Schatten p-class for $1\leq p\leq \infty$. Finally, we determine their trace class and also obtain a connection with the generalized Landau-Pollak-Slepian operators.

双线性乘子的一个同态定理

A Homomorphism Theorem for Bilinear Multipliers

本文证明了局部紧阿贝尔群（LCA）中双线性乘子的一个抽象同态定理。我们还提供了一些应用程序。特别地，我们得到了K的一个双线性抽象形式。强、弱型双线性乘子的de Leeuw定理我们还得到了非紧LCA群上双线性乘子的必要条件，得到了相应算子在重排不变空间乘积上的有界性。我们的研究将欧几里得空间中已有的一些结果推广到一般LCA群的框架下，并得到了拟巴拿赫空间中双线性乘子的有界性的新结果.

Matrix-Valued Gabor Frames over LCA Groups for Operators

G\v avruta studied atomic systems in terms of frames for range of operators (that is, for subspaces), namely $K$-frames, where the lower frame condition is controlled by the Hilbert-adjoint of a bounded linear operator $K$. For a locally compact abelian group G and a positive integer $n$, we study frames of matrix-valued Gabor systems in the matrix-valued Lebesgue space $L^2(G, \mathbb{C}^{n\times n})$ , where a bounded linear operator $Θ$ on $L^2(G, \mathbb{C}^{n\times n})$ controls not only lower but also the upper frame condition. We term such frames matrix-valued $(Θ, Θ^*)$-Gabor frames. F…

Density of spaces of trigonometric polynomials with frequencies from a subgroup in $L^α$-spaces

Let $G$ be an LCA group, $H$ a closed subgroup, $\varGamma$ the dual group of $G$ and $μ$ be a regular finite non-negative Borel measure on $\varGamma$. We give some necessary and sufficient conditions for the density of the set of trigonometric polynomials on $\varGamma$ with frequencies from $H$ in the space $L^α(μ), α\in (0,\infty)$.