摘要
因其在多路复用技术中的潜在应用,超框架(又称向量值框架)和子空间框架受到了众多数学家和工程专家的关注.弱双框架是希尔伯特空间中双框架的推广.本文研究实直线周期子集上的向量值子空间弱Gabor双框架(WGBFs),即L2(S,CL)中的WGBFs,其中S是R上的周期子集.利用Zak变换矩阵方法,得到了WGBFs的刻画,它将构造WGBFs的问题归结为设计有限阶Zak变换矩阵;给出了WGBFs的一个例子定理;导出了WGBFs的一个稠密性定理.
Due to their potential applications in multiplexing techniques, superframes (also called vector-valued frames) and subspace frames have interested many mathe- maticians and engineering specialists. A weak bi-frame is a generalization of a bi-frame in a Hilbert space. This paper addresses vector-valued subspace weak Gabor bi-frames (WGBFs) on periodic subsets of the real line, that is, WGBFs for L2(S, CL) with S being periodic subsets of R. Using Zak transform matrix method, we obtain a charac- terization of WGBFs, which reduces constructing WGBFs to designing Zak transform matrices of finite order; present an example theorem of WGBFs; and derive a density theorem for WGBFs.
作者
赵静
李云章
Jing ZHAO;Yun Zhang LI(College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China)
出处
《数学学报(中文版)》
CSCD
北大核心
2018年第4期651-662,共12页
Acta Mathematica Sinica:Chinese Series
基金
国家自然科学基金资助项目(11271037)