A Little More on Coz-Unique Frames

Coz-unique frames were defined and characterized by Banaschewski and Gilmour (J Pure Appl Algebra 157:1–22, 2001). In this note we give further characterizations of these frames along the lines of characterizations of absolutely z-embedded spaces obtained by Blair and Hager (Math Z 136:41–52, 1974) on the one hand, and by Hager and Johnson (Canad J Math 20:389–393, 1968) on the other. We also extend to frames certain characterizations of z-embedded spaces; namely, we give a characterization of coz-onto frame homomorphisms in terms of normal covers.      

The density theorem for discrete series representations restricted to lattices

This article considers the relation between the spanning properties of lattice orbits of discrete series representations and the associated lattice co-volume. The focus is on the density theorem, which provides a trichotomy characterizing the existence of cyclic vectors and separating vectors, and frames and Riesz sequences. We provide an elementary exposition of the density theorem, that is based solely on basic tools from harmonic analysis, representation theory, and frame theory, and put the results into context by means of examples.     

On dual molecules and convolution-dominated operators

We show that sampling or interpolation formulas in reproducing kernel Hilbert spaces can be obtained by reproducing kernels whose dual systems form molecules, ensuring that the size profile of a function is fully reflected by the size profile of its sampled values. The main tool is a local holomorphic calculus for convolution-dominated operators, valid for groups with possibly non-polynomial growth. Applied to the matrix coefficients of a group representation, our methods improve on classical results on atomic decompositions and bridge a gap between abstract and concrete methods.     

Banach空间的框架和原子分解的摄动及其稳定性

本文利用框架理论对 Banach空间的框架和原子分解的摄动及其稳定性进行了研究,改进并推广了文[5,6]的工作.     

星务1553B总线仿真板卡指令执行的高实时性设计

为实现对某新型卫星总体1553B总线新的“1秒20帧,1帧50条消息”的“帧消息模式”的仿真,研究并实现了一种在满足“帧消息模式”的基础上,使1553B总线仿真板卡的指令执行时间延迟小于1ms的新方法。在分析原星务仿真系统实现机制的基础上,改进软件的整体设计,并在VxWorks下位机中设计了高精度时间获取模块与板卡控制模块等,实现了高精度、短消息传输执行时间的星务1553B总线仿真系统。结果表明：该系统不仅满足对“帧消息模式”的仿真,且将1553B板卡指令执行最大延迟时间缩短为0.713ms,相对于原星务仿真系统中4.5ms的最大延迟,指令执行精度提高了6.5倍以上,为被测设备的故障排查、问题定位提供准确的时间数据支持。     

Embeddings and frames of function spaces

For every Tychonoff space X we denote by Cp(X) the set of all continuous real-valued functions on X with the pointwise convergence topology, i.e., the topology of subspace of RX. A set P is a frame for the space Cp(X) if Cp(X)⊂P⊂RX. We prove that if Cp(X) embeds in a σ-compact space of countable tightness then X is countable. This shows that it is natural to study when Cp(X) has a frame of countable tightness with some compactness-like property. We prove, among other things, that if X is compact and the space Cp(X) has a Lindelöf frame of countable tightness then t(X)?ω. We give some generalizations of this result for the case of frames as well as for embeddings of Cp(X) in arbitrary spaces.