广义Heisenberg群与Shtern问题

Adams-Spanne type estimates for the commutators of fractional type sublinear operators in generalized Morrey spaces on Heisenberg groups

In this paper we give BMO (bounded mean oscillation) space estimates for commutators of fractional type sublinear operators in generalized Morrey spaces on Heisenberg groups. The boundedness conditions are also formulated in terms of Zygmund type integral inequalities.

Heisenberg-李代数弱交换关系中的Hardy测不准原理引理

A Hardy's Uncertainty Principle Lemma in Weak Commutation Relations of Heisenberg-Lie Algebra

在这篇文章中，我们考虑满足一类海森堡-李代数的广义对易关系的线性算子。证明了Hardy测不准原理引理的一个推广不等式。本文还研究了它在时间算子和抽象Dirac算子中的应用。

广义Weyl-Heisenberg群的Gabor型框架

Gabor-type Frames from Generalized Weyl-Heisenberg Groups

本文提出了一种基于广义Weyl-Heisenberg群的Gabor型框架的构造方法。这些后者是通过中心扩展的群体，这是直接产品的局部紧阿贝尔群和他们的south。我们的结果推广了许多结果，出现在文献中，建立了标准魏尔-海森堡群的薛定谔表示的框架。特别是，我们得到了一个推广的结果在\cite{PO}，其中产品$ab$确定是否有可能的Gabor系统$\{E_{mb}T_{na}g \}_{m,n\in \mathbb Z}$是一个帧的$L^2(\mathbb R)$。作为一个特殊的例子的理论，我们研究的情况下，广义Weyl-Heisenberg群建成的$d$维环面。在同样的精神，我们也构造广义平移不变系统。

On Weyl-Heisenberg Frames

In this paper we have generalized and studied the $K$-Weyl-Heisenberg frames, where $K$ is a bounded linear operator on $L^2(\mathbb{R}^d)$. We have obtained necessary and sufficient conditions for acertain system to be a $K$-Weyl-Heisenberg frame. We have also given the invariance property of these $K$-Weyl-Heisenberg frames.

Algebraic analysis on scalar generalized Verma modules of Heisenberg parabolic type I.: $A_n$-series

In the present article, we combine some techniques in the harmonic analysis together with the geometric approach given by modules over sheaves of rings of twisted differential operators ($\mathcal{D}$-modules), and reformulate the composition series and branching problems for objects in the Bernstein-Gelfand-Gelfand parabolic category $\mathcal{O}^\mathfrak{p}$ geometrically realized on certain orbits in the generalized flag manifolds. The general framework is then applied to the scalar generalized Verma modules supported on the closed Schubert cell of the generalized flag manifold $G/P$ for $…

多元Gaussian Weyl-Heisenberg框架的构造（I）

Construction of Multivariate Gaussian Weyl--Heisenberg Frames, (I)

设λ为任意广义高斯压缩相干态，Λ_{αβ}=（α 1 Z \times \cdot \cdot \cdot \times α_{n} \mathbb{Z)\times}（β_{1} \mathbb{Z} \times \cdot \cdot \cdot \times β_{n} \mathbb{Z)} $）为矩形点阵.证明了存在正定辛矩阵M（依赖于λ）使得多元Weyl-Heisenberg系统G（λ，MΛ αβ}）是一个框架.在下一个注中，我们将证明这个结果的逆。